Browsing by Author "Kamugisha Mbabazi Fulgensia"

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Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays
(Hindawi, 2019-02-03) Kamugisha Mbabazi Fulgensia; Mugisha Joseph Y. T.; Kimathi Mark
In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratio Ro is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.
A Mathematical Model Approach for Prevention and Intervention Measures of the COVID–19 Pandemic in Uganda
(Cold Spring Habour Laboratory, 2020-05-11) Kamugisha Mbabazi Fulgensia; Gavamukulya Yahaya; Awichi Richard; Olupot-Olupot Peter; Rwahwire Samson; Biira Saphina; Luboobi Livingstone S.
The human–infecting corona virus disease (COVID–19) caused by the novel severe acute respiratory syndrome corona virus 2 (SARS–CoV–2) was declared a global pandemic on March 11th, 2020. Current human deaths due to the infection have raised the threat globally with only 1 African country free of Virus (Lesotho) as of May 6th, 2020. Different countries have adopted different interventions at different stages of the outbreak, with social distancing being the first option while lock down the preferred option for flattening the curve at the peak of the pandemic. Lock down is aimed at adherence to social distancing, preserve the health system and improve survival. We propose a Susceptible–Exposed–Infected–Expected recoveries (SEIR) mathematical model to study the impact of a variety of prevention and control strategies Uganda has applied since the eruption of the pandemic in the country. We analyze the model using available data to find the infection–free, endemic/infection steady states and the basic reproduction number. In addition, a sensitivity analysis done shows that the transmission rate and the rate at which persons acquire the virus, have a positive influence on the basic reproduction number. On other hand the rate of evacuation by rescue ambulance greatly reduces the reproduction number. The results have potential to inform the impact and effect of early strict interventions including lock down in resource limited settings and social distancing.
Mathematical Models for Influenza a Virus and Pneumococcus: Within-Host and Between-Host Infection
(Pan African University Institute for Basic Sciences, Technology and Innovation, 2019-04) Kamugisha Mbabazi Fulgensia
Infectious diseases have become problematic throughout the world, threatening individuals who come into contact with pathogens responsible for transmitting diseases. Pneumoccocal pneumonia, a secondary bacterial infection follows an influenza A infection, responsible for morbidity and mortality in children, elderly and immuno–comprised groups. The aims of this Thesis are to; develop a mathematical model for within–host co–infection of influenza A virus and pneumococcus, model between–host pneumococcal pneumonia in order to determine the effect of time delays due to latency and seeking medical care, and study the effect of antibiotic resistance awareness and saturated treatment in the control of pneumococcal pneumonia. Analysis of the stability of steady states of influenza A virus and pneumococcal co–infection, pnemococcal pneumonia with time delays and antibiotic resistance awareness is done. The graph theoretic method, combined linear and quadratic Lyapunov functions, Goh–Voltera Lyapunov function are used to get suitable Lyapunov functions for global stability of steady states. The results show that the endemic equilibrium of pneumococcal pneumonia is locally stable without delays and stable if the delays are under conditions. The results suggest that as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability and yields Hopf–bifurcation. The results of influenza A virus and pneumococcal co–infection show that, there exist a biologically important steady state where the two pathogens of unequal strength co–exist and replace each other in the epithelial cell population when the pathogen fitness for each infection exceeds unity. The impact of influenza A virus onto pneumococcus and vice–versa yields a bifurcation state. The results show that, the presence of antibiotic resistance awareness and treatment during the spread of pneumococcal pneumonia drastically reduces the basic reproduction number R0 to less than unity, hence the disease could be eradicated.
Modeling the within-host co-infection of influenza A virus and pneumococcus
(Elsevier, 2018-08-15) Kamugisha Mbabazi Fulgensia; Mugisha J.Y.T.; Kimathi M.
In this paper a nonlinear mathematical model for a within-host co-infection of influenza A virus and pneumococcus is investigated. Conditions that explain the relations amid RIP and its relationship to the global asymptotic stability of the infection-free steady state are discussed. A graph-theoretic method shows that, the unique endemic steady state is globally asymptotically stable. The sensitivity analysis show that, the pathogen fitness for pneumococcus and influenza A virus are most sensitive to maximum number of bacteria an alveolar macrophage can catch, phagocytosis rate, number of infectious IAV and pneumococcus particles liberated from lysis of infected cells and infection rates of influenza A virus and pneumococcal. Numerical results of the model show that, there exists a biologically important steady state where the two infectious pathogens of unequal strength co-exist and replace each other in the epithelial cell population (with pneumococcus leading) when the pathogen fitness for each infection exceeds unity, and we find that this endemic steady state is globally asymptotically stable. Further, the impact of influenza A virus on pneumococcus and vice-visa leads to a bifurcation state.