Mathematical Analysis of the Transmission Dynamics of HIV Syphilis Co-infection in the Presence of Treatment for Syphilis

Abstract

The re-emergence of syphilis has become a global public health issue, and more persons are getting infected, especially in developing countries. This has also led to an increase in the incidence of human immunodeficiency virus (HIV) infections as some studies have shown in the recent decade. This paper investigates the synergistic interaction between HIV and syphilis using a mathematical model that assesses the impact of syphilis treatment on the dynamics of syphilis and HIV co-infection in a human population where HIV treatment is not readily available or accessible to HIV-infected individuals. In the absence of HIV, the syphilis-only model undergoes the phenomenon of backward bifurcation when the associated reproduction number ([Formula: see text]) is less than unity, due to susceptibility to syphilis reinfection after recovery from a previous infection. The complete syphilis-HIV co-infection model also undergoes the phenomenon of backward bifurcation when the associated effective reproduction number ([Formula: see text]) is less than unity for the same reason as the syphilis-only model. When susceptibility to syphilis reinfection after treatment is insignificant, the disease-free equilibrium of the syphilis-only model is shown to be globally asymptotically stable whenever the associated reproduction number ([Formula: see text]) is less than unity. Sensitivity and uncertainty analysis show that the top three parameters that drive the syphilis infection (with respect to the associated response function, [Formula: see text]) are the contact rate ([Formula: see text]), modification parameter that accounts for the increased infectiousness of syphilis-infected individuals in the secondary stage of the infection ([Formula: see text]) and treatment rate for syphilis-only infected individuals in the primary stage of the infection ([Formula: see text]). The co-infection model was numerically simulated to investigate the impact of various treatment strategies for primary and secondary syphilis, in both singly and dually infected individuals, on the dynamics of the co-infection of syphilis and HIV. It is observed that if concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, this will result in a reduction in the incidence of HIV (and its co-infection with syphilis) in the population.

HIV/AIDS-Pneumonia Coinfection Model with Treatment at Each Infection Stage: Mathematical Analysis and Numerical Simulation

“…Nwankwo and Okuonghae [19] formulated and analyzed a mathematical model for the transmission dynamics of syphilis and HIV coinfection in a community to assess the impact of treatment of syphilis on the coendemicity of both diseases in a population where treatment for HIV is not readily available (or easily accessible) but with syphilis treatment sufficiently available. Their syphilis-only model and the full coinfection models undergo the phenomenon of backward bifurcation due to syphilis reinfection after recovery from a previous syphilis infection.…”

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

“…The model undergoes the phenomenon of backward bifurcation and proposed that effective treatment strategies of syphilis in its primary and secondary infected individuals will help reduce the cases. In [26] an investigation was carried out to determine the synergistic interaction between HIV and syphilis using a mathematical model. The paper assessed the impact of syphilis treatment on the dynamics of syphilis and HIV coinfection in a human population where HIV treatment is not readily available or accessible to HIV infected individuals, and they proposed that if a concerted effort is exerted in the treatment of primary and secondary syphilis (in both singly and dually infected individuals), especially with high treatment rates for primary syphilis, then it will result in a reduction in the incidence of HIV (and its coinfection with syphilis) in the population.…”

A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

“…Mathematical models have been used extensively in studying the behaviour of infectious diseases [4, 5, 6, 7, 8, 9, 10, 11]. A lot of models have been developed for the dynamics of the co-infections of two diseases [12, 13, 14, 15, 16, 17, 18]. In this study, we shall be investigating the impact of malaria drug resistance on the co-infection malaria and cholera, using a mathematical model.…”