Browsing by Author "Mugisha, J. Y. T."

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    An age-structured mathematical model for the within host dynamics of malaria and the immune system
    (Springer, 2007) Luboobi, L. S.; Tumwiine, J.; Luckhaus, S.; Mugisha, J. Y. T.
    In the paper, we use a mathematical model to study the population dynamics of replicating malaria parasites and their interaction with the immune cells within a human host. The model is formulated as a system of age-structured partial differential equations that are then integrated over age to obtain a system of nonlinear delay differential equations. Our model incorporates an intracellular time delay between the infection of the red blood cells by the merozoites that grow and replicate within the infected cells to produce new merozoites. The infected red blood cells burst approximately every 48 h releasing daughter parasites to renew the cycle. The dynamical processes of the parasites within the human host are subjected to pressures exerted by the human immunological responses. The system is then solved using a first-order, finite difference method to give a discrete system. Numerical simulations carried out to illustrate stability of the system reveal that the populations undergo damped oscillations that stabilise to steady states.
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    Mathematical model for COVID-19 management in crowded settlements and high-activity areas
    (International Journal of Dynamics and Control, 2021) Ssematimba, A.; Nakakawa, J. N.; Ssebuliba, J.; Mugisha, J. Y. T.
    This paper develops and analyses a habitat area size dependent mathematical model to study the transmission dynamics of COVID-19 in crowded settlements such as refugee camps, schools, markets and churches. The model quantifies the potential impact of physical/social distancing and population density on the disease burden. Results reveal that with no fatalities and no infected entrants, the reproduction numbers associated with asymptomatic and symptomatic cases are inversely proportional to; the habitat area size, and the efforts employed in tracing and hospitalising these cases. The critical habitat area below which the disease dies out is directly proportion to the time taken to identify and hospitalise infected individuals. Results also show that disease persistence in the community is guaranteed even with minimal admission of infected individuals. Our results further show that as the level of compliance to standard operating procedures (SOPs) increases, then the disease prevalence peaks are greatly reduced and delayed. Therefore, proper adherence to SOPs such as use of masks, physical distancing measures and effective contact tracing should be highly enforced in crowded settings if COVID-19 is to be mitigated.
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    On oscillatory pattern of malaria dynamics in a population with temporary immunity
    (Taylor & Francis, 2007) Luboobi, L. S; Tumwiine, J.; Mugisha, J. Y. T.
    We use a model to study the dynamics of malaria in the human and mosquito population to explain the stability patterns of malaria. The model results show that the disease-free equilibrium is globally asymptotically stable and occurs whenever the basic reproduction number, R0 is less than unity. We also note that when R0 . 1, the disease-free equilibrium is unstable and the endemic equilibrium is stable. Numerical simulations show that recoveries and temporary immunity keep the populations at oscillation patterns and eventually converge to a steady state.