Exercise of the book Mathematical Models in Population Biology and Epidemiology, section 9.5

It is all the information that the exercise gives

the second is a SIR model with treatment S - total number of susceptibles I - number of infected or infections T - raster R - total number of Recovered

In the first E - exposed

4. Consider the SEIR model with some infectivity in the exposed period, ds -BS(I +EE), (1) dt de BS(I + E) KE, (2) dt dl KE - al, (3) dt = and the SIR model with treatment, -BS(I +T), (4) ds dt dl dt BS(I +T) - (a + o), (5) dT - 7T. (6) dt Use the parameter values 1 1 B 3000 E = 6 = 3 = 1,6 =1 =1 S . n= and the initial values S(O) = 995, E(0) = 0, 10) = 5, T0 = 0. For each model, (a) Calculate the reproduction number and the epidemic size. (b) Do some numerical simulations to obtain the epidemic size by determining the change in S, the maximum number of infectives by measuring I, and the duration of the epidemic 4. Consider the SEIR model with some infectivity in the exposed period, ds -BS(I +EE), (1) dt de BS(I + E) KE, (2) dt dl KE - al, (3) dt = and the SIR model with treatment, -BS(I +T), (4) ds dt dl dt BS(I +T) - (a + o), (5) dT - 7T. (6) dt Use the parameter values 1 1 B 3000 E = 6 = 3 = 1,6 =1 =1 S . n= and the initial values S(O) = 995, E(0) = 0, 10) = 5, T0 = 0. For each model, (a) Calculate the reproduction number and the epidemic size. (b) Do some numerical simulations to obtain the epidemic size by determining the change in S, the maximum number of infectives by measuring I, and the duration of the epidemic