# American Institute of Mathematical Sciences

October  2018, 23(8): 3137-3151. doi: 10.3934/dcdsb.2017211

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

Received  March 2017 Published  September 2017

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.

Citation: Julia Amador, Mariajesus Lopez-Herrero. Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3137-3151. doi: 10.3934/dcdsb.2017211
##### References:

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##### References:
Final size distribution for several values of $\sigma$
Peak prevalence mass function for several latency rates $\sigma$
Box plot for $M$
$P(M\leq I_{0})$, for $I_{0}=25$ units
Numerical descriptors of Z for several incidence functions
 Mass Action Inhibitory Effect Reaction-Diffusion $P(Z=1)$ $0.168067$ $0.287769$ $0.091743$ $P(Z=100)$ $0.403300$ $2.110\times 10^{-7}$ $0.898751$ $Q_{1}$ $97$ $1$ $100$ $Q_{2}$ $99$ $66$ $100$ $Q_{3}$ $100$ $78$ $100$ $E(Z)$ $79.303911$ $44.601683$ $89.989081$ $\sigma (Z)$ $39.426192$ $37.099482$ $29.828126$
 Mass Action Inhibitory Effect Reaction-Diffusion $P(Z=1)$ $0.168067$ $0.287769$ $0.091743$ $P(Z=100)$ $0.403300$ $2.110\times 10^{-7}$ $0.898751$ $Q_{1}$ $97$ $1$ $100$ $Q_{2}$ $99$ $66$ $100$ $Q_{3}$ $100$ $78$ $100$ $E(Z)$ $79.303911$ $44.601683$ $89.989081$ $\sigma (Z)$ $39.426192$ $37.099482$ $29.828126$
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