Browsing by Author "Tumwiine, Julius"

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    Mathematical models for effectiveness of contact tracing on the onset of an epidemic
    Tumwiine, Julius
    Paper presented at Strathmore International Mathematics Research Conference on July 23 - 27, 2012
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    Modeling and stability analysis of the African swine fever epidemic model
    (Strathmore University, 2019) Byamukama, Michael; Tumwiine, Julius
    In this paper, a mathematical model for the transmission dynamics and control of African swine fever with recruitment of susceptible, exposed and infective domestic pigs into the population is studied using a system of ordinary differential equations. The basic reproduction number Ro for the model was obtained and its dependence on model parameters discussed. Without the inflow of exposed and infective pigs into the population, the model exhibits the disease-free equilibrium Eo and the endemic equilibrium El. The disease-free equilibrium Eo is globally stable if the basic reproduction number Ro < 1 and the disease will be wiped out of the population. If Ro > 1, the endemic equilibrium El is asyrnptotically globally stable and the disease persists in the population. With the influx of exposed and infective domestic pigs, the model has only a unique endemic equilibrium Ee that is globally asymptotically stable and the disease persists. Numerical simulation is carried out to verify the analytical results. It is revealed that with the influx of the exposed and infected pigs, the disease is maintained at endemic equilibrium.
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    Modelling the role of treatment and vaccination in the control of transmission dynamics of pneumonia among children in Uganda
    (Strathmore University, 2017) Kizito, Mohammed; Tumwiine, Julius
    Pneumonia is one of the leading causes of serious illness and deaths among children around the world. Efforts to effectively treat and control the spread of pneumonia is possible if its dynamics is well understood. In this paper, a mathematical model for the transmission dynamics of pneumonia is studied. The population is divided into five epidemiological classes to evaluate the role of treatment and vaccination in mitigating the spread of the disease. A system of differential equations is used to study the disease dynamics. Model analysis is carried out to establish the existence and stability of the steady states. It is revealed that the disease-free equilibrium point is globally stable if and only if the basic reproduction number R0<1 and the disease will be wiped out of the community. If R0>1, the endemic equilibrium point is globally stable and the disease persists at the endemic steady state. We infer the impact of control strategies on the dynamics of the disease through sensitivity analysis of the effective reproduction number Re from which the results showed that the combination of treatment and vaccination can eradicate the pneumonia infection.
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    Modelling transmission and control of African Swine Fever in Uganda with transportation of infected pigs
    (Strathmore University, 2017) Byamukama, Michael; Tumwiine, Julius
    African Swine Fever (ASF) is a devastating haemorrhagic fever of pigs that causes up to 100% mortality, for which there is no vaccine and treatment. Its highly contagious nature and ability to spread over long distances make it one of the most feared diseases, since it’s devastating effects on pig production have been experienced most of sub-Saharan Africa. A mathematical model for spread and control of African Swine Fever with and without transportation of infected pigs is studied using a system of ordinary differential equations. Model analysis is carried out for existence and stability of the equilibrium points to establish the long time behavior of the disease. It is revealed that without inflow of infected pigs into the population, the model has both the disease free and the endemic equilibrium points. The disease free equilibrium point is globally stable when the basic reproduction number is less than one and the disease can be wiped out of the community. If R0>1, the endemic equilibrium point is globally stable and the disease persists in the community. With transportation of infected pigs, the model only has the endemic equilibrium point which is locally stable. This indicates that with constant inflow of infected pigs the disease cannot be wiped out of the community.
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    Trapping the banana weevil, Cosmopolites sordidus, Germar: a mathematical perspective
    (Strathmore University, 2019-08) Kweyunga Eliab Horub; Tumwiine, Julius; Karamura, Eldad
    A logistic equation incorporating trapping is formulated and parameterized to represent the population dynamics of the banana weevil, Cosmopolites Sordidus, (Germar). The steady states are obtained and their asymptotic stability established. The expression for the critical intrinsic growth rate is derived and its implications analyzed. The existence of possible bifurcations is investigated. It is found out that instability increases with the intrinsic growth rate and that as the intrinsic growth rate approaches the critical value, a mathematical catastrophe occurs at which the equilibria annihilate each other and coalesce into one. Numerical simulations are carried out to validate the results.