American Institute of Mathematical Sciences

October  2018, 23(8): 3483-3501. doi: 10.3934/dcdsb.2018250

A stochastic SIRI epidemic model with relapse and media coverage

 1 Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012 Sevilla, Spain 2 Ibn Tofail University, FS, Department of Mathematics, BP 133, Kénitra, Morocco 3 Linnaeus University, Department of Mathematics, 351 95 Växjö, Sweden

Received  January 2018 Published  October 2018 Early access  August 2018

Fund Project: This work has been partially supported by FEDER and the Spanish Ministerio de Economía y Competitividad project MTM2015-63723-P, the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under grant 2010/FQM314 and Proyecto de Excelencia P12-FQM-1492 and the Faculty of Sciences, Ibn Tofail University.

This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we show the existence of a stationary distribution. Numerical simulations are presented to confirm the theoretical results.

Citation: Tomás Caraballo, Mohamed El Fatini, Roger Pettersson, Regragui Taki. A stochastic SIRI epidemic model with relapse and media coverage. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3483-3501. doi: 10.3934/dcdsb.2018250
References:

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References:
Trajectories of stochastic and deterministic systems with the parameters values given in Example 6.1.
Trajectories of stochastic and deterministic systems with the parameters values given in previous Example $2$
The kernel density function estimations of $S(t)$, $I(t)$ and $R(t)$ of stochastic system (1.2) at time $t$ = 9000, based on 10000 stochastic simulation with the parameters values given in Example 3
The kernel density function estimations of $S(t)$, $I(t)$ and $R(t)$ of stochastic system (1.2) at time $t$ = 9500, based on 10000 stochastic simulation with the parameters values given in example 3
Paths simulations of $I(t)$ for stochastic model with the parameters values as in Example 4 and $\beta_2 = 0.01, \; 0.1, \; 0.15$ respectively.
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