Research Articles (Mathematics)
Permanent URI for this collection
Browse
Browsing by Subject "Basic reproduction number"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
Item A model for control of HIV/AIDS with parental care(World Scientific Publishing, 2013) Abiodun, Gbenga Jacob; Marcus, Nizar; Okosun, Kazeem Oare; Witbooi, Peter J.In this study we investigate the HIV/AIDS epidemic in a population which experiences a significant flow of immigrants. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the immigrant youths and how parental care can minimize or prevent the spread of the disease in the population. We analyze the model with both screening control and parental care, then investigate its stability and sensitivity behavior. We also conduct both qualitative and quantitative analyses. It is observed that in the absence of infected youths, disease-free equilibrium is achievable and is globally asymptotically stable. We establish optimal strategies for the control of the disease with screening and parental care, and provide numerical simulations to illustrate the analytic results.Item A model of HIV/AIDS population dynamics including ARV treatment and pre-exposure prophylaxis(SpringerOpen, 2018) Nsuami, Mozart U.; Witbooi, Peter J.Antiretroviral treatment (ART) and oral pre-exposure prophylaxis (PrEP) have recently been used efficiently in management of HIV infection. Pre-exposure prophylaxis consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals. We propose a new model for the transmission of HIV/AIDS including ART and PrEP. Our model can be used to test the effects of ART and of the uptake of PrEP in a given population, as we demonstrate through simulations. The model can also be used to estimate future projections of HIV prevalence. We prove global stability of the disease-free equilibrium. We also prove global stability of the endemic equilibrium for the most general case of the model, i.e., which allows for PrEP individuals to default. We include insightful simulations based on recently published South-African data.Item An SEIR model with infected immigrants and recovered emigrants(Springer Science and Business Media Deutschland GmbH, 2021) Witbooi, Peter J.We present a deterministic SEIR model of the said form. The population in point can be considered as consisting of a local population together with a migrant subpopulation. The migrants come into the local population for a short stay. In particular, the model allows for a constant inflow of individuals into different classes and a constant outflow of individuals from the R-class. The system of ordinary differential equations has positive solutions and the infected classes remain above specified threshold levels. The equilibrium points are shown to be asymptotically stable. The utility of the model is demonstrated by way of an application to measles. © 2021, The Author(s).Item Stochastic modeling of a mosquito-borne disease(Springer Nature, 2020) Abiodun, Gbenga J.; Witbooi, Peter Joseph; van Schalkwyk, Garth J.We present and analyze a stochastic differential equation (SDE) model for the population dynamics of a mosquito-borne infectious disease. We prove the solutions to be almost surely positive and global. We introduce a numerical invariant R of the model with R<1 being a condition guaranteeing the almost sure stability of the disease-free equilibrium. We show that stochastic perturbations enhance the stability of the disease-free equilibrium of the underlying deterministic model. We illustrate the main stability theorem through simulations and show how to obtain interval estimates when making forward projections. We consulted a wide range of literature to find relevant numerical parameter values.