Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate
-
Modeste N'zi
and
Gérard Kanga
Abstract
In this paper, we present an SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with a saturated incidence rate and disease causing death in a population of varying size. We define a parameter ℜ0* from which a study of stability is made. In the deterministic case, we discuss the existence of an endemic equilibria and prove the global stability of the disease-free equilibrium. By introducing a perturbation in the contact rate through a white noise, we consider a stochastic version. We prove the existence of a global positive solution which lives in a certain domain. Thereafter, we prove the global stability nth moment of the system as soon as the intensity of the white noise is below a certain threshold. Finally, we perform some numerical simulations to compare the dynamic behaviors of the deterministic system and the stochastic system.
Funding source: ministère de l'enseignement superieur et de la recherche scientique of Côte d'Ivoire
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© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Berry–Esseen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion
- QWN-first-order Wick differential operators and an associated transport equation
- On the functional Hodrick–Prescott filter with non-compact operators
- Canonical equations K62, K63, K64 and K65 for random non-Hermitian matrices A+B(U+γH)C, the Upturned Stools Law, the Upturned Stool Without Seat Law and Doughnut Law density
- Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate
Articles in the same Issue
- Frontmatter
- Berry–Esseen bounds and almost sure CLT for the quadratic variation of the bifractional Brownian motion
- QWN-first-order Wick differential operators and an associated transport equation
- On the functional Hodrick–Prescott filter with non-compact operators
- Canonical equations K62, K63, K64 and K65 for random non-Hermitian matrices A+B(U+γH)C, the Upturned Stools Law, the Upturned Stool Without Seat Law and Doughnut Law density
- Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate
