An edge-based SIR model for sexually transmitted diseases on the contact network

Asymptotic behavior of the solutions for a stochastic SIRS model with information intervention

In this paper, a stochastic SIRS epidemic model with information intervention is considered. By constructing an appropriate Lyapunov function, the asymptotic behavior of the solutions for the proposed model around the equilibria of the deterministic model is investigated. We show the average in time of the second moment of the solutions of the stochastic system is bounded for a relatively small noise. Furthermore, we find that information interaction response rate plays an active role in disease control, and as the intensity of the response increases, the number of infected population decreases, which is beneficial for disease control.

The dynamics of sexually transmitted diseases with men who have sex with men

In this paper, we give a rather complete analysis for a susceptible-infective sexually transmitted disease (STD) model, where the males are divided into two different groups based on their different sexual orientation. The threshold [Formula: see text] of STD model is obtained. If [Formula: see text], the disease-free equilibrium is globally asymptotically stable. Further, we investigate the existence and stability of the boundary equilibria that characterize the males of the different sexual orientation. We also investigate the existence and stability of the positive equilibrium, which characterizes the possibility of coexistence of male heterosexual and male homosexual. We obtain sufficient and necessary conditions for the existence and global stability of these equilibria. We see that the proportion of heterosexuality in MSM affects the stability of the system. The theoretical results are verified by numerical simulation.

A multilayer temporal network model for STD spreading accounting for permanent and casual partners

Sexually transmitted diseases (STD) modeling has used contact networks to study the spreading of pathogens. Recent findings have stressed the increasing role of casual partners, often enabled by online dating applications. We study the Susceptible-Infected-Susceptible (SIS) epidemic model –appropriate for STDs– over a two-layer network aimed to account for the effect of casual partners in the spreading of STDs. In this novel model, individuals have a set of steady partnerships (links in layer 1). At certain rates, every individual can switch between active and inactive states and, while active, it establishes casual partnerships with some probability with active neighbors in layer 2 (whose links can be thought as potential casual partnerships). Individuals that are not engaged in casual partnerships are classified as inactive, and the transitions between active and inactive states are independent of their infectious state. We use mean-field equations as well as stochastic simulations to derive the epidemic threshold, which decreases substantially with the addition of the second layer. Interestingly, for a given expected number of casual partnerships, which depends on the probabilities of being active, this threshold turns out to depend on the duration of casual partnerships: the longer they are, the lower the threshold.

Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity

A more realistic alcoholism model on scale-free networks with demographic and nonlinear infectivity is introduced in this paper. The basic reproduction number [Formula: see text] is derived from the next-generation method. Global stability of the alcohol-free equilibrium is obtained. The persistence of our model is also derived. Furthermore, the SAITS model with nonlinear infectivity is also investigated. Stability of all the equilibria and persistence are also obtained. Some numerical simulations are also presented to verify and extend our theoretical results.