Browsing by Author "Witbooi, Peter Joseph"

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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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    Does phylogeny have an influence on the date of first description? A comparative study of the world's fishes
    (Elsevier, 2020) Beukes, Brandon; Witbooi, Peter Joseph; Gibbons, Mark J.
    The process of species description is not random, and understanding the factors that influence when a species is first described (the date of first description, DoFD) allows us to target environments and/or species' traits to increase our knowledge of diversity. Such studies typically correlate species traits (e.g. maximum size, occupational depth) against DoFD, forgetting that species are not statistically independent of each other, owing to the inheritance of shared characteristics. A recent study of extant fishes by Costello et al. (2015) identified depth and geographic range size as the most important (of many) predictors of the DoFD, implying that newly described species will likely occupy restricted areas and occur deep in the water column. However, these authors failed to accommodate for “identity by descent” in their analyses.
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    Mathematical analysis of TB model with vaccination and saturated incidence rate
    (Hindawi, 2020) Witbooi, Peter Joseph; Mengistu, Ashenafi Kelemu
    The model system of ordinary differential equations considers two classes of latently infected individuals, with different risk of becoming infectious. The system has positive solutions. By constructing a Lyapunov function, it is proved that if the basic reproduction number is less than unity, then the disease-free equilibrium point is globally asymptotically stable. The Routh-Hurwitz criterion is used to prove the local stability of the endemic equilibrium when R0 > 1. The model is illustrated using parameters applicable to Ethiopia. A variety of numerical simulations are carried out to illustrate our main results.
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    A population model for the 2017/18 listeriosis outbreak in South Africa
    (PLoS One, 2020-03-12) Witbooi, Peter Joseph; Africa, Charlene Wilma Joyce; Christoffels, Alan; Ahmed, Ibrahim Hussin Ibrahim
    We introduce a compartmental model of ordinary differential equations for the population dynamics of listeriosis, and we derive a model for analysing a listeriosis outbreak. The model explicitly accommodates neonatal infections. Similarly as is common in cholera modeling, we include a compartment to represent the reservoir of bacteria. We also include a compartment to represent the incubation phase. For the 2017/18 listeriosis outbreak that happened in South Africa, we calculate the time pattern and intensity of the force of infection, and we determine numerical values for some of the parameters in the model. The model is calibrated using South African data, together with existing data in the open literature not necessarily from South Africa. We make projections on the future outlook of the epidemiology of the disease and the possibility of eradication.
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    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.