Transmission dynamics of Trichomonas vaginalis: A mathematical approach

Abstract

Despite the availability of treatment that is effective, Trichomonas vaginalis infections are still high. A deterministic model for transmission dynamics of Trichomonas vaginalis is presented as a system of non-linear differential equations. Analysis of the reproduction number has shown that an increase in the number of straight women (non-lesbians) infected result in an increase in the number of lesbians infected. This suggests that straight women are turning into lesbians already infected. The disease-free equilibrium is shown to be globally asymptotically stable when the corresponding reproduction number is less than unity. Analytical results and numerical simulations both show that treatment is able to control Trichomonas vaginalis infections. This suggests an effective control of trichomoniasis rests in encouraging and persuading sexual partners of those displaying symptoms to seek treatment. Failure for the asymptomatic to seek treatment (mostly males given that the majority of males does not show symptoms) will continue to fuel the infection.

Invariant Region, Endemic Equilibria and Stability Analysis

“…[3,5,4,6] For these examples all state variables and parameters are assumed to be non-negative, since the models monitors human population. Moreover, the infections themselves do not kill, hence there is no disease induced death.…”

“…Therefore the system of equations that describes or models trichomoniasis or chancroid transmission dynamics is dissipative, and for an endemic equilibrium point of such a system, there exist a strict Lyapunov function . [3,5,4,6] Using this, the conclusion that the endemic equilibrium point is globally and locally asymptotically stable for can be drawn for the "Transmission dynamics of trichomoniasis in bisexuals", for instance. [3] …”

Mathematical analysis of a model for the transmission dynamics of Trichomonas vaginalis (TV) and HIV coinfection

“…The model extends the model for the transmission dynamics of TV and HIV in Bhunu and Mushayabasa, and is to the author's knowledge is the first to incorporate control strategies of TV and HIV coinfection in a population. In addition, it extends numerous TV models in the literature such as those in Bhunu and Mushayabasa and Bowden and Garnett by (inter alia): Allowing for TV transmission by treated individuals ( η ≠ 0), this is not considered in Bhunu and Mushayabasa, Subdividing the infected population with TV into counselled and noncounselled individuals, this is not considered in Bhunu and Mushayabasa, Assessing various control strategies for TV (counselling, treatment, and condom use). …”

Transmission dynamics of Trichomonas vaginalis and HIV/AIDS coinfection

“…Here we attempt to give mathematical analysis of it taking into consideration effects of differential infectivity patterns between males and females. Here we modify earlier papers [6,2] with some simplifications to come up with a distinct HIV and TV coinfection model. The rest of the manuscript is organised as follows: In the next section we describe and present the model.…”