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Type:

Package

Title:

Dynamic Models in Epidemiology

Depends:

R (≥ 3.6)

Imports:

deSolve, reshape2, ggplot2, grid

Description:

Mathematical models of infectious diseases in humans and animals. Both, deterministic and stochastic models can be simulated and plotted.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

LazyLoad:

yes

URL:

https://github.com/oswaldosantos/EpiDynamics

Version:

0.3.1

Date:

2020-02-12

RoxygenNote:

7.0.2

NeedsCompilation:

Packaged:

2020-02-12 20:26:15 UTC; oswaldo

Author:

Oswaldo Santos Baquero [aut, cre], Fernando Silveira Marques [aut]

Maintainer:

Oswaldo Santos Baquero <baquero@usp.br>

Repository:

CRAN

Date/Publication:

2020-02-13 09:40:05 UTC

The EpiDynamics Package

Description

Mathematical models of infectious diseases in humans and animals. Both, deterministic and stochastic models can be simulated and plotted.

Details

Package:	EpiDynamics
Type:	Package
Version:	0.3.1
Date:	2020-02-11
Depends:	R (>= 3.6)
Imports:	deSolve, reshape2, ggplot2, grid
License:	GPL (>= 2)
LazyLoad:	yes
URL:	http://oswaldosantos.github.io/EpiDynamics
Authors:	Oswaldo Santos Baquero baquero@usp.br
	Fernando Silveira Marques fernandosix@gmail.com
Maintainer:	Oswaldo Santos Baquero oswaldosant@gmail.com

Partial immunity model that cycles (P 4.2).

Description

Solves multi-strain where the strains are arranged in a circle and each strain offers partial immunity (in terms of reduced transmission) to its neighbours.

Usage

MultiStrainPartialImmunity(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 2 vectors and 2 values in the following order: beta, gamma, mu and a. The first element of each vector corresponds to the first strain, the second element to the second strain and so on. mu is the per capita death rate and alpha is the modified transmission rate due to partial immunity.

init

vector with 3 vectors in the following order: S, P and L. The first element of each vector corresponds to the first strain, the second element to the second strain and so on. Si + Pi + Li = 1 but sum(Si) could be greater than 1.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 4.2 from page 123 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = rep(40, 4), gamma = rep(9.98, 4),
                       mu = 0.02, a = 0.4 )

initials <- c(S = c(0.08, 0.1, 0.1, 0.11),
                       P = c(0.4, 0.3, 0.3, 0.29),
                       L = c(0.15, 0.02, 0.1, 0.01))

# Solve and plot.
mlti.strain.pi <- MultiStrainPartialImmunity(pars = parameters, 
                                             init = initials, 
                                             time = 0:200)
PlotMods(mlti.strain.pi, variables = c('L1', 'L2', 'L3', 'L4'), grid = FALSE)

Plot results of capm model functions

Description

Plot results of EpiDynamics' functions.

Usage

PlotMods(
  model.out = NULL,
  variables = NULL,
  x.label = NULL,
  y.label = NULL,
  legend.title = "variable",
  line.size = 1,
  text.size = 14,
  grid = TRUE,
  bifur = FALSE
)

Arguments

model.out

output of aEpiDynamics' function.

variables

column index for the variables in model.out to be plotted.

x.label

string with the name of x axis.

y.label

string with the name of y axis.

legend.title

string with the legend title.

line.size

scalar to define the thick of the lines (points for bifurcations) to be plotted.

text.size

scalar to define the size of axis texts and titles.

grid

logical to indicate if each variable must be plotted in a separated panel.

bifur

logical to indicate if model.out represent a bifurcation.

Examples

# Parameters and initial conditions.
parameters <- list(beta0 = 17 / 13, beta1 = 0.1, gamma = 1 / 13,
                   omega = 2 * pi / 365, mu = 1 / (50 * 365))

initials <- c(S = 1 / 17, I = 1e-4, 
              R = 1 - 1 / 17 - 1e-4)

# Solve the system.
sir.sinusoidal.forcing <- SIRSinusoidalForcing(pars = parameters, 
                                               init = initials, 
                                               time = 0:(60 * 365))
PlotMods(sir.sinusoidal.forcing)                                          
                                               
# Solve bifurcation dynamics for 20 years.
# If max(time) < 3650, bifurcation dynamics are solved for 3650 time-steps.
parameters2 <- list(beta0 = 17 / 13, beta1 = seq(0.001, 0.251, by = 0.001),
                   gamma = 1 / 13, omega = 2 * pi / 365, mu = 1 / (50 * 365))
# Uncomment the following lines:
# bifur <- SIRSinusoidalForcing(pars = parameters2, 
#                               init = initials,
#                               time = 0:(20 * 365))
# PlotMods(bifur, bifur = TRUE)

SEIR model (2.6).

Description

Solves a SEIR model with equal births and deaths.

Usage

SEIR(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 4 values: the per capita death rate (and the population level birth rate), the transmission rate, the movement form exposed to infectious and the recovery rate. The names of these values must be "mu", "beta", "sigma" and "gamma", respectively.

init

vector with 3 values: the initial proportion of proportion of susceptibles, exposed, infectious and recovered. The names of these values must be "S", "E", "I" and "R", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

All parameters must be positive and S + E + I + R <= 1.

Details

This is the R version of program 2.6 from page 41 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second to fifth column contain the proportion of susceptibles, exposed, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(mu = 1 / (70 * 365), beta = 520 / 365,
                    sigma = 1 / 14, gamma = 1 / 7)
initials <- c(S = 0.1, E = 1e-04, I = 1e-04, R = 1 - 0.1 - 1e-4 - 1e-4)

# Solve and plot.
seir <- SEIR(pars = parameters, init = initials, time = 0:(60 * 365))
PlotMods(seir)

SEIR model with 4 age classes and yearly aging (P 3.4).

Description

Solves a SEIR model with four different age-groups and yearly "movements" between the groups mimicking the school year

Usage

SEIR4AgeClasses(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with: a matrix with the transmission rates, the rate at which individuals move from the exposed to the infectious classes, the recovery rate, a vector with death rates in each age group, and a vector with birth rates into the childhood class. The names of these elements must be "beta", "sigma", "gamma", "mu", and "nu", respectively, see example.

init

vector with 16 values: initial proportions of the population that are susceptible, exposed, infectious and recovered in a particular age group. The vector must be named, see example. Requirements: S + E + I <= n for each age group and all values must be positive.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.4 from page 87 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All rates are specified in days. Moreover, a vector n with the proportion of each age group. All parameters must be positive.

Value

list of class SolveSIR4ACYA. The first element, *$model, is the model function. The second, third and fourth elements are vectors (*$pars, *$init, *$time, respectively) containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, exposed, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- list(beta = matrix(c(2.089, 2.089, 2.086, 2.037,
                                   2.089, 9.336, 2.086, 2.037,
                                   2.086, 2.086, 2.086, 2.037,
                                   2.037, 2.037, 2.037, 2.037),
                                 nrow = 4, ncol = 4),
                    sigma = 0.125, gamma = 0.2,
                    mu = c(0, 0, 0, 1) / (55 * 365),
                    nu = c(1 / (55 * 365), 0, 0, 0),
                    n = c(6, 4, 10, 55) / 75)
                          
initials <- c(S = c(0.05, 0.01, 0.01, 0.008), 
              E = c(0.0001, 0.0001, 0.0001, 0.0001),
              I = c(0.0001, 0.0001, 0.0001, 0.0001),
              R = c(0.0298, 0.04313333, 0.12313333, 0.72513333))

# Solve and plot.
# Uncomment the following lines (running it takes more than a few seconds):
# seir4.age.classes <- SEIR4AgeClasses(pars = parameters, 
#                                      init = initials,
#                                      time = 0:36500)
# PlotMods(seir4.age.classes,
#          variables = c('I1', 'I2', 'I3', 'I4'), grid = F)

SEIR model with n stages (P 3.5).

Description

Solves a SEIR model with multiple stages to create gamma-distributed exposed and infectious periods.

Usage

SEIRnStages(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 5 values: the transmission rate, the removal or recovery rate, the death rate (we assume that nu=mu), the number of stages in the infected period and the number of stages in the exposed period. The names of these elements must be "beta", "gamma", "mu", "n" and "m", respectively, see example. All rates are specified in days and all rates and parameters must be positive, moreover, m < n.

init

vector with n + 1 values: initial proportions of the population that are susceptible and infected. The vector must be named, see example. Requirements: S + all Infected <= 1.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.5 from page 94 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are vectors (*$pars, *$init, *$time, respectively) containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles and infected.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
n <- 13
parameters <- list(beta = 17 / 5, gamma = 1 / 13, mu = 1 / (55 * 365),
                   n = n, m = 8)

initials <- c(S = 0.05, I = 0.00001 * rep(1, n) / n)

# Solve and plot.
# Uncomment the following lines (running it takes more than a few seconds):
# seir.n.stages <- SEIRnStages(pars = parameters, 
#                              init = initials, 
#                              time = seq(1, 30 * 365, 1))
# PlotMods(seir.n.stages, variables = 2)
# PlotMods(seir.n.stages, variables = 3:13, grid = F)

Simple SIR model (P 2.1).

Description

Solves a simple SIR model without births or deaths.

Usage

SIR(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 2 values: the transmission and recovery rates. The names of these values must be "beta", and "gamma", respectively.

init

vector with 3 values: the initial proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.1 from page 19 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and S + I + R <= 1.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors *$pars, *$init and *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1.4247, gamma = 0.14286)
initials <- c(S = 1 - 1e-06, I = 1e-06, R = 1 - (1 - 1e-06 - 1e-06))

# Solve and plot.
sir <- SIR(pars = parameters, init = initials, time = 0:70)
PlotMods(sir)

SIR model with 2 age classes (P 3.3).

Description

Solves a SIR model two different age-groups.

Usage

SIR2Stages(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 8 values: 4 transmission rates, 1 recovery rate, rate at which children mature, death rate in the childhood group and death rate in the adult group. The names of these values must be "betaCC","betaCA","betaAC", "betaAA", "gamma", "lC","muC" and "muA", respectively. The letters after the word "beta" denote transmission to any group from any group, e.g., "betaCA" represent transmission to children group from adult group. All parameters must be positive. Parameters "nC" na "nu" (proportion of the population that are in the childhood group and birth rate into the childhood class, respectively) are not defined explicitly but calculated as: nC = muA/(lC+muA) and nu = (lC+nuA)nC. All rates are specified in years and all parameters must be positive

init

vector with 4 values: the initial proportion of the population that are both susceptible and in the childhood group, the initial proportion of the population that are both infectious and in the childhood group, the initial proportion of the population that are both susceptible and in the adult group, and the initial proportion of the population that are both infectious and in the adult group. The names of these values must be "SC", "IC", "SA" and "IA", respectively. Requirements: SC + IC <= nC, and SA + IA <= nA = 1 - nC.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.3 from page 79 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(betaCC = 100, betaCA = 10, betaAC = 10, betaAA = 20,
                gamma = 10, lC = 0.0666667, muC = 0.0, muA = 0.016667)
initials <- c(SC = 0.1, IC = 0.0001, SA = 0.1, IA = 0.0001)

# Solve the system.
sir2stages <- SIR2Stages(pars = parameters, 
                          init = initials, time = seq(0, 100, 0.01))

SIR model with two types of imports (P 6.6).

Description

Solves a model with two types of stochastic imports and demographic stochasticit

Usage

SIR2TypesImports(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 5 parameters: transmission rate, recovery rate and per capita death rate. The names of these values must be "beta", "gamma", "mu", "epsilon" and "delta" respectively. All parameters must be positive. The birth rate is assumed to be constant and equal to mu * N, therefore preventing extinction of the host population.

init

vector with 3 values: the initial population size that are susceptible, infectious and the total population size. The names of these values must be "X", "Y" and "N", respectively. All initial conditions must be positive and all refer to integer numbers.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 6.6 from page 210 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first, second and third elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fourth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the number of susceptibles, infectious, recovered and boolean for epsilon and delta imports.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1, gamma = 0.1, mu = 5e-4,
                epsilon = 2e-5, delta = 0.01)
initials <- c(X = 5, Y = 2, N = 50)

# Solve and plot.
sir.2types.imports <- SIR2TypesImports(parameters, initials, 2 * 365)
PlotMods(sir.2types.imports)

SIR model with constant additive noise (P 6.1).

Description

Solves a SIR model with constant additive noise added to the transmission rate.

Usage

SIRAdditiveNoise(pars = NULL, init = NULL, time = NULL, step = 1, ...)

Arguments

pars

vector with 5 values: the transmission rate, the recovery rate, the birth (deadth) rate, the amount of noise experienced in the transmission rate and the population size assumed to be constant. The names of these values must be "beta", "gamma", "mu", "noise", and "N" respectively.

init

vector with 2 values: the initial number of susceptibles and infectious. The names of these values must be "X", and "Y", respectively. "X" and "Y" must be positive and are numbers not proportions.

time

time sequence for which output is wanted; the first value of times must be the initial time.

step

step size to set the integration step and to scale the noise term.

...

further arguments passed to ode function.

Details

This is the R version of program 6.1 from page 194 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors *$pars, *$init and *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second and third columns contain the number of susceptibles and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1, gamma = 1 / 10, mu = 1 / (50 * 365),
                noise = 10, N = 1e6)
initials <- c(X = 1e5, Y = 500)

# Solve and plot.
sir.additive.noise <- SIRAdditiveNoise(pars = parameters, init = initials,
                                       time = 0:(2 * 365), step = 1)
PlotMods(sir.additive.noise)

SIR model with births and deaths (P 2.2).

Description

Solves a simple SIR model with equal births and deaths.

Usage

SIRBirthDeath(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 3 values: the per capita death rate (equal to the population level birth rate), the transmission rate, and the recovery rate. The names of these values must be "mu", "beta", and "gamma", respectively.

init

vector with 3 values: the initial proportion of proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.2 from page 27 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and S + I + R <= 1.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors *$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(mu = 1 / (70 * 365),
                       beta = 520 / 365, gamma = 1 / 7)
initials <- c(S = 0.1, I = 1e-4, R = 1 - 0.1 - 1e-4)

# Solve and plot.
sir.birth.death <- SIRBirthDeath(pars = parameters, init = initials, 
                                 time = 0:(60 * 365))
PlotMods(sir.birth.death)

SIR model with carrier state (2.7).

Description

Solves a SIR model with carrier state.

Usage

SIRCarrierState(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 6 values: the per capita death, transmission, infectious-recovery and carrier-recovery rates, the proportion of reduction in transmission from carriers compared with infectious and the proportion of infectious that become carriers. The names of these values must be "mu", beta", "gamma", "Gamma", "epsilon" and "rho", respectively.

init

vector with 4 values: the initial proportion of proportion of susceptibles, infectious, carriers and recovered. The names of these values must be "S", "I", "C" and "R", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.7 from page 44 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and S + I + C + R <= 1.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second to fifth column contain the proportion of susceptibles, infectious, cariers and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(mu = 1 / (50 * 365), beta = 0.2, 
                    gamma = 0.1, Gamma = 0.001, 
                    epsilon = 0.1, rho = 0.4)
initials <- c(S = 0.1, I = 1e-4, C = 1e-3, R = 1 - 0.1 - 1e-4 - 1e-3)

# Solve the system.
sir.carrier.state <- SIRCarrierState(pars = parameters,
                                     init = initials, time = 0:60)
PlotMods(sir.carrier.state)

SIR model with demographic stochasticity (P 6.4).

Description

Solves a SIR model with demographic stochasticity

Usage

SIRDemogStoch(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 3 parameters: transmission rate, recovery rate and per capita death rate. The names of these values must be "beta", "gamma" and "mu", respectively. All parameters must be positive and all rates are specified in days. The birth rate is assumed to be constant and equal to mu * N, therefore preventing extinction of the host population.

init

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 6.4 from page 203 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first, second and third elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fourth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1, gamma = 1 / 10, mu = 5e-4)
initials <- c(X = 500, Y = 25, N = 5e3)

# Solve and plot.
sir.demog.stoch <- SIRDemogStoch(pars = parameters, 
                                 init = initials, time = 2 * 365)
PlotMods(sir.demog.stoch)

SIR model with disease induced mortality: Density-dependent transmission (P 2.3).

Description

Solves a SIR model with a probability of mortality, and unequal births and deaths.

Usage

SIRInducedMortality(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 5 values: the probability that an infected individual dies from the disease before recovering, the per capita death rate from natural causes, the population level birth rate, the transmission rate, and the recovery rate. The name of these values must be: "rho", "mu", "nu", "beta", and "gamma", respectively. All parameters must be positive.

init

vector with 3 values: the initial number of susceptibles, infectious and recovered. The names of these values must be "X", "Y" and "Z", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.3 from page 35 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(rho = 0.5, mu = 1 / (70 * 365), nu = 1 / (70 * 365),
                      beta = 520 / 365.0, gamma = 1 / 7)
initials <- c(X = 0.2, Y = 1e-4, Z = 1 - 0.2 - 1e-4)

# Solve and plot.
# Uncomment the following lines (running it takes more than a few seconds):
# sir.induced.mortality <- SIRInducedMortality(pars = parameters, 
#                                  init = initials, 
#                                  time = 0:1e5)
# PlotMods(sir.induced.mortality)

SIR model with disease induced mortality: frequency-dependent transmission (P 2.4).

Description

Solves a SIR model with a probability of mortality, and unequal births and deaths

Usage

SIRInducedMortality2(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 5 values: the probability than an infected individual dies from the disease before recovering, the per capita death rate from natural causes, the population level birth rate, the transmission rate, and the recovery rate. The names of these values must be "rho", "mu", "nu", "beta", and "gamma", respectively. All parameters must be positive.

init

vector with 3 values: the initial number of susceptibles, infectious and recovered. The names of these values must be "X", "Y" and "Z", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.4 from page 36 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters<- c(rho = 0.5,mu = 1 / (70 * 365.0),nu= 1 / (70 * 365.0),
                      beta = 520 / 365.0, gamma = 1 / 7)
initials <- c(X = 0.2, Y = 1e-4, Z = 1 - 0.2 - 1e-4)

# Solve and plot.
sir.induced.mortality2 <- SIRInducedMortality2(pars = parameters, 
                                 init = initials, 
                                 time = 0:1e4)
PlotMods(sir.induced.mortality2)

SIR model with partial immunity (P 4.1).

Description

Solves a model with partial immunitiy.

Usage

SIRPartialImmunity(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 9 values: the death, birth, transmission and recovery rates, the modified susceptiblity to strain i for those individuals recovered from the other strain and the modified transmission rate of strain i from those individuals that have recovered from the other strain. The name of these values must be "mu", "v", "beta1", "beta2", "gamma1", "gamma2", "alpha1", "aplha2", "a1", "a2". The numbers 1 and 2 at the end of parameters names stand for strain 1 and strain 2.

init

vector with 8 values: In this formulation NAB refers to the proportion of the population who are A with respect to strain 1 and B with respect to strain 2. Thus, initial values must be named: "NSS", "NIS", "NRS", "NRI", "NSI", "NSR", "NIR" and "NRR". The sum of initial values must be <= 1.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 4.1 from page 118 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(mu = 1 / (70 * 365), beta1 = 260 / 365, 
                beta2 = 520 / 365, gamma1 = 1 / 7, 
                gamma2 = 1 / 7, alpha1 = 0.5,
                alpha2 = 0.4, a1 = 0.4, a2 = 0.5)

initials <- c(NSS = 0.1, NIS = 1e-4, NRS = 0.02, NRI = 0,
              NSI = 1e-4, NSR = 0.5, NIR = 0, NRR = 0.3798)

# Solve and plot.
sir.partial.immunity <- SIRPartialImmunity(pars = parameters, 
                                           init = initials,
                                           time = 0:(100 * 365))
PlotMods(sir.partial.immunity, variables = c('NIS', 'NIR'), grid = FALSE)

SIR model with Scaled additive noise (P 6.2).

Description

Solves a SIR model with scaled additive noise.

Usage

SIRScaledAdditiveNoise(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 5 parameters: transmission rate, recovery rate, per capita death rate, the total population size and the number of steps that will change noise term. The names of these values must be "beta", "gamma", "mu", "N" and "step", respectively. All parameters must be positive and all rates are specified in days. The birth rate is assumed to be constant and equal to mu * N, therefore preventing extinction of the host population. Noise terms are generated as a function of the time step and its magnitude is a function of the rate of each process.

init

vector with 2 values: the initial population size that are susceptible and infectious. The names of these values must be "X" and "Y", respectively. All initial conditions must be positive.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 6.2 from page 197 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1, gamma = 1 / 10, mu = 1 / (50 * 365),
                N = 1e6, step = 1)
initials <- c(X = 1e5, Y = 500)

# Solve and plot.
sir.scaled.additive.noise <- 
SIRScaledAdditiveNoise(pars = parameters, 
                       init = initials, time = 5 * 365)
PlotMods(sir.scaled.additive.noise)

SIR model with sinusoidal births (P 5.3).

Description

Solves a SIR model with sinusoidal forcing of the birth rate.

Usage

SIRSinusoidalBirth(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with: the transmission rate, the mean birth rate, a scalar (or a vector to create bifurcations) with the amplitude of sinuoidal forcing for the birth rate, the frequency of the oscillations, the per capita death rate and the recovery rate. The names of these values must be "beta", "alpha0", "alpha1", "w", "mu" and "gamma", respectively. All rates must be specified in days and alpha1 <= 1.

init

vector with 3 values: the initial proportion of susceptibles and infectious. The names of these values must be "S" and "I", respectively. All parameters must be positive and S + I <= 1.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 5.3 from page 184 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani. To create bifurcations, alpha1 must be a vector. For bifurcations, if max(time) < 3650), time is defined as c(0:3650). Here, different to the original Python code, we wrote equations for the R population as R = 1 - S - I.

Value

list. The first element, *$model, is the model function. The second element is a list with the the *$pars argument. The third and fourth elements are the vectors (*$init, *$time, containing the init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

                                  
# Parameters and initial conditions (bifurcation plot of infectious)
parameters <- list(beta = 17 / 13, alpha0 = 1 / (50 * 365),
                   alpha1 = 0.25, w = 2 * pi / 365 ,
                   mu = 1 / (50 * 365), gamma =  1 / 13)

parameters2 <- list(beta = 17 / 13, alpha0 = 1 / (50 * 365),
                   alpha1 = seq(0, 0.99, 0.01), w = 2 * pi / 365 ,
                   mu = 1 / (50 * 365), gamma =  1 / 13)

initials <- c(S = 1 / 17, I = 1e-4, R =  1 - (1 / 17 + 1e-4))

# Solve and plot.
sir.sinusoidal.birth <- SIRSinusoidalBirth(pars = parameters,
                                           init = initials, 
                                           time = 0:(20 * 365))
PlotMods(sir.sinusoidal.birth)

# Bifurcations
# Uncomment the following lines (running it takes more than a few seconds):
# bifurcation <- SIRSinusoidalBirth(pars = parameters2,
#                                   init = initials, 
#                                   time = 0:(20 * 365))
# PlotMods(bifur, bifur = TRUE)

SIR model with sinusoidal forcing (P 5.1).

Description

Solves a SIR model with sinusoidal forcing of the transmission rate.

Usage

SIRSinusoidalForcing(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with 4 values: the death rate, the mean transmission rate, a scalar (or a vector to create bifurcations) with the amplitude of sinusoidal forcing, the frequency of oscillations and the recovery rate. The names for these values must be: "mu", "beta0", "beta1", "omega" and "gamma", respectively.

init

vector with 3 values: initial proportion of proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively. All parameters must be positive and S + I <= 1.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 5.1 from page 160 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

When beta1 is a vector in pars, it must be a sequence between 0 and 1.

Value

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- list(beta0 = 17 / 13, beta1 = 0.1, gamma = 1 / 13,
                   omega = 2 * pi / 365, mu = 1 / (50 * 365))

initials <- c(S = 1 / 17, I = 1e-4, 
              R = 1 - 1 / 17 - 1e-4)

# Solve and plot.
sir.sinusoidal.forcing <- SIRSinusoidalForcing(pars = parameters, 
                                               init = initials, 
                                               time = 0:(60 * 365))
PlotMods(sir.sinusoidal.forcing)

# Solve bifurcation dynamics for 20 years.
# If max(time) < 3650, bifurcation dynamics are solved for 3650 time-steps.
parameters2 <- list(beta0 = 17 / 13, beta1 = seq(0.001, 0.251, by = 0.001),
                   gamma = 1 / 13, omega = 2 * pi / 365, mu = 1 / (50 * 365))
# Uncomment the following lines (running it takes more than a few seconds):
# bifur <- SIRSinusoidalForcing(pars = parameters2, 
#                               init = initials,
#                               time = 0:(20 * 365))
# PlotMods(bifur, bifur = TRUE)

SIR model with tau leap method (P 6.5).

Description

SIR model with demographic stochasticity approximated using the tau-leap method and assuming Poisson distributions.

Usage

SIRTauLeap(pars, init, end.time)

Arguments

pars

vector with 5 values: the transmission, recovery and death rates, the population size assumed to be constant and the time step. The names of these values must be "beta", "gamma", "mu", "N" and "tau" respectively.

init

vector with 3 values: the initial number of susceptibles, infectious and recovered, respectively. The names of these values must be "X", "Y" and "Z" respectively.

end.time

end time to be simulated.

Details

This is the R version of program 6.5 from page 204 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first three elements are the vectors *$pars, *$init and *$time, containing the pars, init and end.time arguments of the function. The fourth element *$results is a data.frame with up to as many rows as time steps determined by the parameters tau and end.time. The first column contains the time steps. The second, third and fourth columns contain the number of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1, gamma = 1 / 10, mu = 5e-4, N = 50, tau = 1)
initials <- c(X = 5, Y = 1, Z = 44)
end.time <- 2 * 365

# Solve and plot.
sir.demog.stoch <- SIRTauLeap(pars = parameters, init = initials,
                              end.time = end.time)
PlotMods(sir.demog.stoch)

SIR model with corrected term-time forcing (P 5.2).

Description

Solves a SIR model with corrected term-time forcing of the transmission rate.

Usage

SIRTermTimeForcing(
  pars = NULL,
  init = NULL,
  term.times = terms,
  cicles = 10,
  low.term.first = TRUE,
  ...
)

Arguments

pars

list with 4 values: the mean transmission rate, a scalar (or a vector to create bifurcations) with the amplitude of sinusoidal forcing, the removal recovery rate, and the per capita death rate. The names for these values must be: "beta0", "beta1", "gamma", and "mu", respectively. All parameters must be positive and beta1 <= 1.

init

vector with 3 values: the initial proportion of proportion of susceptibles, infectious and recovered. The names of these values must be "S", "I" and "R", respectively. S + I + R <= 1.

term.times

vector indicating the term times (see details and example).

cicles

value indicating how many times term.times must be simulated (see details and example).

low.term.first

logical. If TRUE (default), the first term-time is considered -1, the second 1, the tirth -1 and so on. When FALSE, the first term-time is 1, the second -1, and so on (see example).

...

further arguments passed to ode function.

Details

This is the R version of program 5.2 from page 171 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

This model is based on the behaviour os measles and other child-hood diseases. Transmission rate is low during term == -1 (e.g. holydas term) and high during term == 1 (e.g. school term). We can define the year as the temporal unit of cicles and each cicle is composed by a term-time sequence (see example).

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are vectors (*$pars, *$init, *$time, respectively) containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

## Parameters and initial conditions.
initials <- c(S = 1/17, I = 1e-4, R = 1 - 1/17 - 1e-4)
parameters <- list(beta0 = 17 / 13, beta1 = 0.25,
                gamma = 1 / 13, mu = 1 / (50 * 365))

## Term-times and cycles
# In a year-unit cicle, holidays happen for example
# between days 1 and 6, 101 and 115, 201 and 251,
# 301 and 307 and 308 and 365. 
# Setting low.term.first == TRUE (default) we define the
# previous term-times as low terms.
# Simulate 10 years.
terms <- c(1, 6, 100, 115, 200, 251, 300, 307, 356, 365)
cicles <- 10

# Solve and plot.
sir.term.time.forcing <- SIRTermTimeForcing(pars = parameters,
                                            init = initials,
                                            term.times = terms,
                                            cicles = 10)
PlotMods(sir.term.time.forcing)

# Solve bifurcation dynamics for 20 years.
# If the number of time-units per cicle (e.g. days) times
# the number of cicles (e.g. number of days) is less
# than 3650, bifurcation dynamics are solved for 3650
# time-steps
parameters2 <- list(beta0 = 17 / 13,
                beta1 = seq(0, 0.3, by = 0.001),
                gamma = 1 / 13, mu = 1 / (50 * 365))
# Uncomment the following lines (running it takes more than a few seconds):
# bifur <- SIRTermTimeForcing(pars = parameters2, init = initials,
#                             term.times = terms, cicles = 10)
# PlotMods(bifur, bifur = TRUE)

SIR model for mosquito vectors (P 4.4).

Description

Solves a simple SIR model for mosquito vectors.

Usage

SIRVector(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 8 values: the human mortality rate (muH), the mosquito mortality rate (muM), the human birth rate (vH), the mosquito birth rate (vM), the transmission probability from humans to mosquitos following a bite (betaHM), the transmission probability from mosquitos to humans, following a bite (betaMH), the human recovery rate (gamma) and the rate at which humans are bitten (r). Abbreviations in parenthesis indicate the names which must be given to the values.

init

vector with 4 values: the initial numbers of susceptible humans, susceptible mosquitos, infectious humans and infectious mosquitos. The names of this values must be "XH", "XM", "YH" and "YM", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 4.2 from page 123 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are vectors (*$pars, *$init, *$time, respectively) containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(muH = 5.5e-5, muM = 0.143,
                vH = 5.5e-2, vM = 1.443e3, 
                betaHM = 0.5, betaMH = 0.8, 
                gamma = 0.033, r = 0.5 / 1e3)

initials <- c(XH = 1e3, XM = 1e4, YH = 1, YM = 1)

# Solve and plot.
sir.vector <- SIRVector(pars = parameters,
                        init = initials,
                        time = 0:1000)                                 
PlotMods(sir.vector)

Simple SIS model (P 2.5).

Description

Solves a simple SIS model without births or deaths.

Usage

SIS(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 2 values: the transmission and recovery rates. The names of these values must be "beta", and "gamma", respectively.

init

vector with 2 values: the initial proportion of proportion of susceptibles and infectious. The names of these values must be "S" and "I", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 2.5 from page 39 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and S + I <= 1.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second and third columns contain the proportion of susceptibles and infectious.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 1.4247, gamma = 0.14286)
initials <- c(S = 1 - 1e-06, I = 1e-06)

# Solve and plot.
sis <- SIS(pars = parameters, init = initials, time = 0:70)
PlotMods(sis)

SIS model with 2 risk groups (P 3.1).

Description

Solves a SIS model with high-risk (H) and low-risk (L).

Usage

SIS2RiskGroups(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 6 values: 4 transmission rates, 1 recovery rate and the proportion of the population that are in the high-risk group. The names of these values must be "betaHH","betaHL","betaLL", "betaLH", "gamma" and "nH", respectively. The letters after the word "beta" denote transmission to any group from any group, e.g., "betaHL" represent transmission to high-risk group from low-risk group. All parameters must be positive.

init

vector with 2 values: the initial proportion of infectious in the high-risk group and the intial proportion of infectious in the low-risk group. The names of these values must be "IH" and "IL", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.1 from page 58 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive and nH <= 1, IH(0) <= nH, IL(0) <= 1-nH.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles and infectious.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(betaHH = 10.0, betaHL = 0.1, betaLH = 0.1,
                betaLL = 1.0, gamma = 1, nH = 0.2)
initials <- c(IH = 0.00001, IL = 0.001)

# Solve and plot.
sis2risk.groups<- SIS2RiskGroups(pars = parameters,
                                 init = initials, time = 0:15)
PlotMods(sis2risk.groups, variables = c('IL', 'IH'), grid = FALSE)

SIS model with demographic stochasticity (P 6.3).

Description

SIS model with event-driven or demographic stochasticity.

Usage

SISDemogStoch(pars, init, end.time)

Arguments

pars

vector with 3 values: the transmission and recovery rates and the population size assumed to be constant. The names of these values must be "beta", "gamma", and "N" respectively.

init

initial number of infectious.

end.time

end time to be simulated.

Details

This is the R version of program 6.3 from page 202 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first three elements are the vectors *$pars, *$init and *$time, containing the pars, init and end.time arguments of the function. The fourth element *$results is a data.frame with up to as many rows as time steps created during the stochastic simulations. The second column contains the number of infectious.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(beta = 0.03, gamma = 1 / 100, N = 100)
initials <- 70

# Solve and plot.
sis.demog.stoch <- SISDemogStoch(pars = parameters,
                                 init = initials, end.time = 10 * 365)
PlotMods(sis.demog.stoch)

Pairwise SIS approximation model (P 7.8).

Description

Solves a pairwise approximation to the SIS model on a random network of N individuals, each with n contacts.

Usage

SISPairwiseApprox(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 4 values: the transmission rate across a contact, the recovery rate for infectious individuals, the number of connections per individual in the population and the number of individuals in the population. The names of these values must be "tau", "gamma", "n" and "N" respectively.

init

vector with 3 values: the initial number of of susceptibles, infectious and susceptible-infectious pairs. The names of these values must be "X", "Y" and "XY", respectively.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 7.8 from page 285 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors *$pars, *$init and *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the number of susceptibles, infectious and susceptible-infectious pairs.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
n <- 4; N <- 1e4; Y <- 1; X <- N - Y
parameters <- c(tau = 0.1, gamma = 0.05, n = n, N = N)
initials <- c(X = X, Y = Y, XY = n * Y * X / N)

# Solve and plot.
sis.pairwise.approx <- SISPairwiseApprox(pars = parameters,
                                         init = initials, time = 0:100)
PlotMods(sis.pairwise.approx)

Rabbit Hemorrhagic Disease model with sinusoidal transmission rate and per capita birth rate (P 5.4).

Description

Solves the Rabbit Hemorrhagic Disease, in which both transmission rate and birth rates can be seasonally forced.

Usage

SISinusoidalTransmBrith(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with: the mean transmission rate, the amplitude of sinuoidal forcing (transmission), the mean birth rate, the amplitude of sinuoidal forcing for the birth rate, the frequency of the oscillations, the recovery rate, the per capita death rate, the mortality rate due to infection, and the carrying capacity. The names of these values must be "beta0", "beta1", "alpha0", "alpha1", "w", "gamma", "mu", "m" and "K", respectively. All parameters must be positive, alpha1, beta1 <= 1.

init

vector with 3 values: the initial numbers of susceptible hosts (rabbits), infectious hosts (rabbits) and total population size. The names of these values must be "X", "Y" and "N", respectively. All initial values must be positive and X(0) + Y(0) <= N(0).

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 5.4 from page 186 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second element is a list with the *$pars argument. The third and fourth elements are the vectors *$init and *$time, containing the init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. Second, third and fourth columns contain the number of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- list(beta0 = 0.936, beta1 = 0.1, alpha0 = 0.02, alpha1 = 0.1,
                   w = 2 * pi / 365, gamma = 0.025,  mu = 0.01, m = 0.475,
                   K = 10000)
initials <- c(X = 0.5, Y = 0.01, N = 0.6)

# Solve and plot.
sis.rhdm <- SISinusoidalTransmBrith(pars = parameters,
                                    init = initials,
                                    time = 0:(60 * 365))
PlotMods(sis.rhdm)

SIS model with multiple risk groups (P 3.2).

Description

Solves a SIS model with n different risk-groups.

Usage

SISnRiskGroups(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

list with: the number of risk groups, a (m x m) matrix with the transmission rates, a vector with the recovery rates (one for each risk group) and a vector with the proportions of the population that are in each risk group. The names of these elements must be "m", "beta", "gamma" and "n", respectively (see example). All rates are specified in years.

init

vector with m * 2 values: the initial proportions of susceptibles and infectious in each risk group. The names of these values must be "S1",..., "Sm" and "I1",..., "Im", respectively (see example). All initial states must be positive and Si + Ii = ni, i= 1, ..., m.

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.2 from page 64 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

All parameters must be positive, and ni <= 1, sum(ni) = 1, i = 1, ..., m.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles and infectious of each risk group.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
tmp <-matrix(c(0, 3, 10, 60, 100))
beta <- 0.0016 * tmp %*% t(tmp)
parameters <- list(m = 5, beta = beta, 
                   gamma = c(0.2, 0.2, 0.2, 0.2, 0.2),
                   n = c(0.06, 0.31, 0.52, 0.08, 0.03))
initials <- c(I = c(0, 0, 0, 0, 1e-5))

# Solve and plot.
sis.n.riks.groups <- SISnRiskGroups(pars = parameters, 
                                    init = initials, 
                                    time = 0:30)
PlotMods(sis.n.riks.groups, grid = FALSE)

SIR model with 2 age classes (P 3.3).

Description

Solves a SIR model two different age-groups.

Usage

sir2AgeClasses(pars = NULL, init = NULL, time = NULL, ...)

Arguments

pars

vector with 8 values: 4 transmission rates, 1 recovery rate, rate at which children mature, death rate in the childhood group and death rate in the adult group. The names of these values must be "betaCC","betaCA","betaAC", "betaAA", "gamma", "lC","muC" and "muA", respectively. The letters after the word "beta" denote transmission to any group from any group, e.g., "betaCA" represent transmission to children group from adult group. All parameters must be positive. Parameters "nC" na "nu" (proportion of the population that are in the childhood group and birth rate into the childhood class, respectively) are not defined explicitly, but calculated as: nC = muA/(lC+muA) and nu = (lC+nuA)nC. All rates are specified in years and all parameters must be positive

init

time

time sequence for which output is wanted; the first value of times must be the initial time.

...

further arguments passed to ode function.

Details

This is the R version of program 3.3 from page 79 of "Modeling Infectious Disease in humans and animals" by Keeling & Rohani.

Value

list. The first element, *$model, is the model function. The second, third and fourth elements are the vectors (*$pars, *$init, *$time, containing the pars, init and time arguments of the function. The fifth element *$results is a data.frame with up to as many rows as elements in time. First column contains the time. The following columns contain the proportion of susceptibles, infectious and recovered.

References

Keeling, Matt J., and Pejman Rohani. Modeling infectious diseases in humans and animals. Princeton University Press, 2008.

Examples

# Parameters and initial conditions.
parameters <- c(betaCC = 100, betaCA = 10, betaAC = 10, betaAA = 20,
                gamma = 10, lC = 0.0666667, muC = 0.0, muA = 0.016667)
initials <- c(SC = 0.1, IC = 0.0001, SA = 0.1, IA = 0.0001)

# Solve and plot.
sir2AgeClasses <- sir2AgeClasses(pars = parameters, 
                          init = initials, time = seq(0, 100, 0.01))
PlotMods(sir2AgeClasses, variables = c('IA', 'IC'), grid = FALSE)

The EpiDynamics Package

Description

Details

Partial immunity model that cycles (P 4.2).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Plot results of capm model functions

Description

Usage

Arguments

Examples

SEIR model (2.6).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

SEIR model with 4 age classes and yearly aging (P 3.4).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

SEIR model with n stages (P 3.5).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Simple SIR model (P 2.1).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

SIR model with 2 age classes (P 3.3).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

SIR model with two types of imports (P 6.6).

Description

Usage

Arguments

Details

Value

References

See Also

Examples

SIR model with constant additive noise (P 6.1).

Description

Usage

Arguments

Details

Value

References

See Also

Examples