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

Huan Yang; Long Zhang; Zhidong Teng; Huan Yang; Long Zhang; Zhidong Teng

doi:10.3934/era.2026122

Electronic Research Archive

2026, Volume 34, Issue 4: 2631-2651. doi: 10.3934/era.2026122

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

1.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
2.
The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China
3.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China

Received: 16 January 2026 Revised: 13 March 2026 Accepted: 17 March 2026 Published: 26 March 2026

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.
- gonorrhea,
- incubation delay,
- sexual structure,
- uniform persistence,
- optimal control strategy
Citation: Huan Yang, Long Zhang, Zhidong Teng. The influence of sexual structure and dual incubation delays on spreading dynamics and optimal control of a gonorrhea model[J]. Electronic Research Archive, 2026, 34(4): 2631-2651. doi: 10.3934/era.2026122

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Abstract

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.

References

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