Remove all objects from workspace.

remove (list = objects() )

Load add-on packages - deSolve - contains lsoda function - differential equation solver.

library (deSolve)
## 
## Attaching package: 'deSolve'
## 
## The following object is masked from 'package:graphics':
## 
##     matplot

creat equations

sis_model = function (current_timepoint, state_values, parameters)
{  
  # create state variables (local variables)
  Sm = state_values [1]        # susceptibles men
  Im = state_values [2]        # infectious men
  Sw = state_values [3]       # susceptibles women
  Iw = state_values [4]       # infectious women
  
  with (
    as.list (parameters), # variable names within parameters can be used 
         { # compute derivatives
           dSm = (-beta_mw * Sm * Iw) + (gamma * Im)
           dIm = ( beta_mw * Sm * Iw) - (gamma * Im)
           dSw = (-beta_wm * Sw * Im) + (gamma * Iw)
           dIw = ( beta_wm * Sw * Im) - (gamma * Iw)
           
           
           # combine results
           results = c (dSm, dIm, dSw, dIw)
           list (results)
         } 
        )
}

Parameters

contact_rate_men_acquirefrom_women = 50/365 # number of contacts per day
contact_rate_women_acquirefrom_men = 50/365 # number of contacts per day
transmission_probability_men_from_women = 0.05 # transmission probability
transmission_probability_women_from_men = 0.1 # transmission probability
infectious_period = 365            # infectious period (day)

Compute values of beta (tranmission rate) and gamma (recovery rate).

beta_mw_value = contact_rate_men_acquirefrom_women * transmission_probability_men_from_women

beta_wm_value = contact_rate_women_acquirefrom_men * transmission_probability_women_from_men

gamma_value = 1 / infectious_period

Compute Ro - Reproductive number.

Ro.m = beta_mw_value / gamma_value
Ro.W = beta_wm_value / gamma_value

Disease dynamics parameters.

parameter_list = c (beta_mw = beta_mw_value, beta_wm = beta_wm_value ,gamma = gamma_value)

Initial values for sub-populations.

A = 10000 # susceptible men
B = 11000 # susceptible women
C = 1  # infectious men
D = 1 # infectious women

Compute total population.

N = A+B+C+D

Initial state values for the differential equations.

initial_values = c (Sm = A/N, Im = C/N, Sw = B/N, Iw = D/N )

Output timepoints.

timepoints = seq (0,3650,by = 1)

Simulate the SIS epidemic.

output = lsoda (initial_values, timepoints, sis_model, parameter_list)

Plot dynamics of Susceptibles sub-population.

plot (Sm ~ time, data = output, type='b', col = 'blue')

Plot dynamics of Infectious sub-population.

plot (Im ~ time, data = output, type='b', col = 'red')

Plot dynamics of Susceptibles sub-population.

plot (Sw ~ time, data = output, type='b', col = 'purple')

Plot dynamics of Infectious sub-population.

plot (Iw ~ time, data = output, type='b', col = 'green')

Plot dynamics of Susceptibles and infectious sub-populations in the same plot.

# susceptible men over time
plot (Sm ~ time, data = output, type='b', ylim = c(-0.2,0.8), col = 'blue', ylab = 'S, I, S', main = 'SIS Heterogeneous') 
text(1500,0.4, "Sm", col = 'blue')

# remain on same frame
par (new = TRUE)    


# susceptible women over time
plot (Sw ~ time, data = output, type='b', ylim = c(-0.2,0.8), col = 'purple', ylab = '', axes = FALSE) 
text(1500,0.6, "Sw", col = 'purple')

# remain on same frame
par (new = TRUE) 

# infectious men over time
plot (Im ~ time, data = output, type='b', ylim = c(-0.2,0.8), pch = 18,  col = 'red', ylab = '', axes = FALSE) 
text(1500,0.05, "Im", col = 'red')

# remain on same frame
par (new = TRUE) 

# infectious women over time
plot (Iw ~ time, data = output, type='b', ylim = c(-0.2,0.8), col = 'green', ylab = '', axes = FALSE) 
text(1500,-0.05, "Iw", col = 'green')

Description: SIS heterogeneous model is used to describe a hetero sexaully transmitted infection. The model has two compartments (S and I) of each sex (male and female). All equations of each sex must be combined for construct this model. Number of susceptible of men and women decrease over the time period since they will get the infection from infected hosts, on the other hand, once everyone got infected number of infected men and women will increase.