Mathematical analysis and optimal control interventions for sex structured syphilis model with three stages of infection and loss of immunity

Advances in Difference Equations

article

Momoh, Abdulfatai Atte¹  Bala, Yusuf¹  Washachi, Dekera Jacob¹  Déthié, Dione² 

[1] Department of Mathematics, Modibbo Adama University of Technology;Cheikh Anta Diop University

关键词: Stability;    Hamiltonian;    Transmission;    Equilibrium states;    Epidemiology;    Invariant region;   

DOI  :  10.1186/s13662-021-03432-7

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this study, we develop a nonlinear ordinary differential equation to study the dynamics of syphilis transmission incorporating controls, namely prevention and treatment of the infected males and females. We obtain syphilis-free equilibrium (SFE) and syphilis-present equilibrium (SPE). We obtain the basic reproduction number, which can be used to control the transmission of the disease, and thus establish the conditions for local and global stability of the syphilis-free equilibrium. The stability results show that the model is locally asymptotically stable if the Routh–Hurwitz criteria are satisfied and globally asymptotically stable. The bifurcation analysis result reveals that the model exhibits backward bifurcation. We adopted Pontryagin’s maximum principle to determine the optimality system for the syphilis model, which was solved numerically to show that syphilis transmission can be optimally best control using a combination of condoms usage and treatment in the primary stage of infection in both infected male and female populations.

【 授权许可】

CC BY