Asymptotic behavior of a multigroup SIS epidemic model with stochastic perturbation

Abstract

In this paper, we introduce stochasticity into a multigroup SIS model. We present the sufficient condition for the exponential extinction of the disease and prove that the noises significantly raise the threshold of a deterministic system. In the case of persistence, we prove that there exists an invariant distribution which is ergodic. MSC: 60H10; 93E15; 34E10

Imprecise parameters for near‐optimal control of stochastic SIV epidemic model

“…Most biological systems always assume that parameters of the model are accurate . However, it is impossible because of the unavoidable errors and the lack of sufficient information in the measurement process and so on.…”

“…For deterministic SIV epidemic models, Liu et al researched the properties of global positive solutions of SIV system, and Lin et al considered the properties of asymptotically stable and stationary distribution of SIV epidemic system. For stochastic models, Fu et al built sufficient conditions for stochastic SIV system extinction and persistence. Tornatore et al prove the stability and the disease‐free equilibrium of the stochastic SIV epidemic model.…”

“…Recently, the epidemiological models with control variables have been analyzed by some authors . For example, Chen et al studied a disease dynamic model and derived necessary conditions of optimal controls.…”

“…Recently, the epidemiological models with control variables have been analyzed by some authors. 5,12,[14][15][16][17][18][19] For example, Chen et al 19 studied a disease dynamic model and derived necessary conditions of optimal controls. Kumar et al 14 combined treatment with information influence as control intervention and presented a deterministic SIRS epidemic model.…”

Dynamical analysis of a ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting in a random environment

“…Later stochastic models have also shown to be advantageous when the contact structure in the community contains small complete graphs; households and other local social networks are common examples. Indeed, by introducing stochastic environmental noise, some scholars have proposed some stochastic epidemic models [14][15][16][17][18][19], stochastic population models [20][21][22][23][24][25][26][27][28]. Liu [21,22] established sufficient and necessary criteria for the existence of optimal harvesting policy and obtained optimal harvesting effort and the maximum value of the cost function in a random environment.…”