Media alert in an SIS epidemic model with logistic growth

Abstract

In general, media coverage would not be implemented unless the number of infected cases reaches some critical number. To reflect this feature, we incorporate the media effect and a critical number of infected cases into the disease transmission rate and consider an susceptible-infected-susceptible epidemic model with logistic growth. Our model analysis shows that early media alert and strong media effects are preferable to decrease the numbers of infected cases at endemic equilibria. Furthermore, we noticed that the model may have up to three endemic equilibria and bi-stability can occur in a threshold interval for the critical number. Note that the interval depends on parameters for the focal disease and the media effect. It is possible to roughly estimate the interval for re-emerging diseases in a given region. Therefore, the result could be useful to health policymakers. Global stability is also obtained when the model admits a unique endemic equilibrium. ARTICLE HISTORY

Qualitative Analysis of Both Hyperbolic and Non-hyperbolic Equilibria of a SIRS Model with Logistic Growth Rate of Susceptibles and Inhibitory Effect in the Infection

“…Again, if we fix the parameters k, β, d, γ and µ as listed in Table 3 then Figure 5(b) shows that for every values of r, E 2 cannot be stable if α > 1. 26. In fact, E 2 is not feasible for α > 1.…”

“…To formulate the compartmental model two important factors play the crucial role: one is the growth rate of susceptible class and the other is the rate of infection [9][10][11][12][13][14][15][16][17][18][19]. The authors usually consider the constant growth rate [17], exponential growth rate and logistic growth rate [9][10][11][12]26]. The logistic growth rate is considered in those models where food supply, space capacity or carrying capacities of the system are limited.…”

The persistence and extinction of a stochastic SIS epidemic model with Logistic growth

“…In the previous section, we have investigated the persistence of the solution to model (9). In this section, we shall prove that the density of the infected individuals will be driven to extinction with a negative exponential power under some simple assumptions.…”

“…In this section, we shall investigate the persistence property of model (9). The solution of model (9) is said to be persistent in the mean if …”

“…As an example of this phenomenon, Ngonghala et al pointed out that malaria in developing countries took place with growth of local population size. When it concerns the variable population size, some recent literature works, such as Ngonghala et al [7], Busenberg and Driessche [8], Wang et al [9], Zhao et al [10], Zhu and Hu [11], Li et al [12], had considered the effect of population size on the epidemic dynamics. We would like to mention the work by Wang et al [9], in which they constructed an SIS epidemic model under the assumption that the susceptible individuals followed the Logistic growth:…”