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

Julia Amador; Mariajesus Lopez-Herrero

doi:10.3934/dcdsb.2017211

Article Contents

2018, Volume 23, Issue 8: 3137-3151. Doi: 10.3934/dcdsb.2017211

This issue Previous Article Continuous and discrete one dimensional autonomous fractional ODEs Next Article Method of sub-super solutions for fractional elliptic equations

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

Faculty of Statistical Studies, Complutense University of Madrid, Ciudad Universitaria, 28040 Madrid, Spain

Received: February 28, 2017

Early access: August 2017

Published: August 2018

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Abstract

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.

Keywords:

Stochastic epidemic model,
nonlinear incidence,
limited resources,
cumulative and maximum number of infected.

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

Citation:

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

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

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Figure 3. Box plot for $M$

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

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Table 1. Numerical descriptors of Z for several incidence functions

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

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