An SIRS (Susceptible-Infectious-Recovered-Susceptible) model with sexual structure and dual incubation delays was proposed to characterize the effects of homosexual and heterosexual behaviors on the transmission dynamics and optimal control of gonorrhea. First, the nonnegativity and boundedness of solutions were obtained, and the basic reproduction number ${\mathcal{R}}_0$ was calculated as well. Second, local and global asymptotical stability of the disease-free equilibrium was established if ${\mathcal{R}}_0<1$. If ${\mathcal{R}}_0>1$ the disease was uniformly persistent, and there existed at least one endemic equilibrium. An optimal control strategy was derived based on sensitivity analysis and practical intervention policy. Finally, the theoretical findings were illustrated through numerical simulations, revealing that targeted management of male infected individuals can markedly diminish gonorrhea prevalence, while disregarding the incubation periods tended to substantially overestimate the epidemic scale.

This paper establishes an HIV infection model, which includes wild-type and drug-resistant strains, and the dynamic behavior of infection model with saturated incidence and distributed delays is investigated. The nonnegativity and boundedness of solutions, and the existence of equilibria are obtained. The threshold criteria for the local and global asymptotic stability of equilibria and the uniform persistence of the model are established by using the linearization method, constructing Lyapunov functions and applying the theory of persistence in dynamical systems. Moreover, the numerical examples illustrate that the positive equilibrium may be globally asymptotically stable.

In this paper, we propose a delayed HBV infection model with saturation incidence and adaptive immune response, considering two infection pathways. The model includes five compartments of uninfected hepatocytes, infected hepatocytes, free HBV virus, CTL immune response, and antibodies. Define five thresholds: infection basic reproductive number R₀, antibody immune reproductive number R₁, CTL immune reproductive number R₂, CTL immune competition reproductive number R₃ and antibody immune competition reproductive number R₄. Five kinds of equilibria of the model are obtained. By analyzing the characteristic equations and constructing suitable Lyapunov functionals and Lasalle invariance principles, the criteria for local and global asymptotic stability of each equilibrium are established.