Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate

N'zi, Modeste; Kanga, Gérard

doi:10.1515/rose-2016-0005

Cited by 6 publications

(6 citation statements)

References 21 publications

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“…There are numerous ways of deriving a stochastic model from the deterministic model: parametric perturbation stochastic model which introduces diffusion coefficient of the specific parameter(s) of interest to be perturbed, while on other hands non-parametric perturbation stochastic model involves adding Brownian processes to each differentia equation and assume that each compartment has uncertainty (Nsengiyumva et al, 2013;N'zi and Kanga, 2016;Miao et al, 2017). Several authors have undertaken various stochastic models for HIV and AIDS including authors such as (Mbogo et al, 2013;Zhang and Zhou, 2019;Fan et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

Tengaa¹,

Mwalili²,

Orwa³

2020

IJSP

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In this paper, we investigated on the stochastic epidemic model by incorporating viral load detectability. We derived HIV and AIDS stochastic model from the deterministic counterpart model and presented a stochastic threshold in terms of stochastic basic reproduction number. We showed that R_s^0 < 1 then the disease dies out exponentially and when R_s^0 > 1 the disease persists in the population. We further derived the existence and uniqueness, extinction and persistence properties of the stochastic model models, then the numerical simulation is done by using Milsten’s numerical scheme. The finding shows that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterparts which provide some useful control strategies to eradicate the disease

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Section: Introductionmentioning

confidence: 99%

Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

Tengaa¹,

Mwalili²,

Orwa³

2020

IJSP

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“…This type of effect is termed as the "crowing effect" or "protection measure". The term like 1+bI in the denominator of the incidence term measures the inhibition effect from the behavioral change of the susceptible individuals when the number of infectious individuals increases or from the crowding effect of the infective individuals [30] . Kar and Mondal [25] used the saturation effect in the form pSI 1 + αS , where α was defined as the half saturation constant.…”

Section: Introductionmentioning

confidence: 99%

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

Ghosh¹,

Susmita²

2018

CMST

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In this paper we have considered an SIR model with logistically grown susceptible in which the rate of incidence is directly affected by the inhibitory factors of both susceptible and infected populations and the protection measure for the infected class. Permanence of the solutions, global stability and bifurcation analysis in the neighborhood of equilibrium points has been investigated here. The Center manifold theory is used to find the direction of bifurcations. Finally numerical simulation is carried out to justify the theoretical findings.

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“…(1.1) is said to be the SIRS model with unbounded incidence function for ℓ > h, saturated incidence function for ℓ = h, and nonmonotone incidence function for ℓ < h, respectively; see e.g. [14,19,22,25,29] and references within.…”

Section: Introductionmentioning

confidence: 99%

“…The deterministic SIRS models (1.1) have been extended in several different ways into stochastic or random counterparts. One of them is to perturb the deterministic models by white noises, see, for instance, [3,16,22,26,32] upon asymptotic analysis. Whereas, with regard to deterministic SIRS models or stochastic counterparts perturbed by white noises, the environment is assumed to be constant.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of SIRS Models in State-dependent Random Environments

Bao

Shao

2018

Preprint

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The extinction and persistence of infective individuals are closely related to the random change of the environment. In this paper, via the random/stochastic SIRS models, we analyze qualitatively and quantitatively the impact caused by the random change of the environment. Our contributions consist in (i) giving some sufficient conditions on extinction (persistence) of the infectious individuals even though they are persistent (resp. extinct) in certain fixed environments; (ii) revealing the influence of random switching of incidence functions on extinction for the infectious individuals, which has not been studied before; (iii) establishing a criterion to judge extinction of the infectious individuals for a range of random/stochastic SIRS models with state-dependent switching via a stochastic comparison for functionals of jump processes. Moreover, some examples are set to illustrate the applications of our theory.

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Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model with saturated incidence rate

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 ℜ

Cited by 6 publications

References 21 publications

Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

Stochastic Modeling for HIV and AIDS Epidemics With Viral Load Detectability

Global Stability Analysis of Logistically Grown SIR Model with Loss of Immunity, Inhibitory Effect, Crowding Effect and its Protection Measure

Asymptotic Behavior of SIRS Models in State-dependent Random Environments

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