The influence of sexual structure and dual incubation delays on spreading dynamics and optimal control of a gonorrhea model

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.