Article Contents
Article Contents

# Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources

• The paper deals with a stochastic SEIR model with nonlinear incidence rate and limited resources for a treatment. We focus on a long term study of two measures for the severity of an epidemic: the total number of cases of infection and the maximum of individuals simultaneously infected during an outbreak of the communicable disease. Theoretical and computational results are numerically illustrated.

Mathematics Subject Classification: 60J22, 60J28, 92D30.

 Citation:

• Figure 1.  Final size distribution for several values of $\sigma$

Figure 2.  Peak prevalence mass function for several latency rates $\sigma$

Figure 3.  Box plot for $M$

Figure 4.  $P(M\leq I_{0})$, for $I_{0}=25$ units

Table 1.  Numerical descriptors of Z for several incidence functions

 Mass Action Inhibitory Effect Reaction-Diffusion $P(Z=1)$ $0.168067$ $0.287769$ $0.091743$ $P(Z=100)$ $0.403300$ $2.110\times 10^{-7}$ $0.898751$ $Q_{1}$ $97$ $1$ $100$ $Q_{2}$ $99$ $66$ $100$ $Q_{3}$ $100$ $78$ $100$ $E(Z)$ $79.303911$ $44.601683$ $89.989081$ $\sigma (Z)$ $39.426192$ $37.099482$ $29.828126$

Figures(4)

Tables(1)