Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

Abstract

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

Global exponential stability of multi-group models with multiple dispersal and stochastic perturbation based on graph-theoretic approach

“…From the application point of view, it is of great practical significance to take stochastic perturbation into account in MGM. In the past few years, MGM with stochastic perturbation have attracted many researchers' attention and many results, which can supply a theoretical basis for investigating ecology, epidemiology, and so on, have been reported in the literature (see [20][21][22][23][24]). However, to the best of the authors' knowledge, stochastic perturbation has rarely been considered in MGM with single dispersal, let alone MGMMD.…”

The most common friend first immunization

“…Therefore, designing a highly effective immunization strategy has been of wide concern. [28][29][30][31][32][33] Typical immunization strategies are as follows: random immunization, [34] targeted immunization, [35] acquaintance immunization, [36] and other immunization strategies. [37,38] Random immunization is a simple strategy, which completely randomly selects a part of nodes over the whole network, and carries out immunization, but it is almost immunization of all the nodes to obtain a better immune effect.…”

Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

“…In infectious disease modelling, the model's parameters have become a crucial factor to ensure that the models have some realistic significance and may give some reasonable description. [14] In the previous models, the infection rate K and the viral production rate α are considered to be constant coefficients. However, they are time-varying due to the effect of RTI and PI drugs.…”