Browsing by Author "Nsuami, Mozart Umba"

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    Control and elimination in an SEIR model for the disease dynamics of Covid-19 with vaccination
    (AIMS Press, 2023) Witbooi, Peter Joseph; Vyambwera, Sibaliwe Maku; Nsuami, Mozart Umba
    COVID-19 has become a serious pandemic affecting many countries around the world since it was discovered in 2019. In this research, we present a compartmental model in ordinary differential equations for COVID-19 with vaccination, inflow of infected and a generalized contact rate. Existence of a unique global positive solution of the model is proved, followed by stability analysis of the equilibrium points. A control problem is presented, with vaccination as well as reduction of the contact rate by way of education, law enforcement or lockdown. In the last section, we use numerical simulations with data applicable to South Africa, for supporting our theoretical results. The model and application illustrate the interesting manner in which a diseased population can be perturbed from within itself.
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    Modeling the population dynamics of HIV/AIDS with opportunistic infections at the severe stage of HIV
    (American Institute of Mathematical Sciences, 2025) Nsuami, Mozart Umba; Witbooi, Peter Joseph
    In this paper, we present a deterministic model for the population dynamics of HIV/AIDS, wherein some individuals at the severe symptomatic phase of HIV develop serious opportunistic infections (OIs) such cryptococcal, tuberculous, pneumococcal, and other bacterial meningitis due to an inappropriate treatment or lack of counseling. OIs are responsible for significant mortality and disability on individuals with HIV in many countries. Cryptococcal meningitis (CM) is among frequent OIs responsible for significant mortality and disability of individuals with HIV in limited resource settings. However, there are also cases of high mortality due to CM on HIV-uninfected individuals, but the burden of CM is more frequent in people living with HIV. We proved the global stability of the disease-free as well as the endemic equilibrium points. In addition, we performed the study of sensitivity analysis of the basic reproduction number with the parameters of the model as well as with some compartmental classes. We illustrated our theoretical results by way of numerical simulations using a projection on the HIV historical data of South Africa since 2024. Our analysis showed that a combination of ART and OI specific treatments may reduce the number of death related cases.