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

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    Modeling traffic flow and management at un-signalized, signalized and roundabout road intersections
    (Academia, 2005) Luboobi, Livingstone S; Kakooza, R.; Mugisha, J.Y.T.
    Traffic congestion continues to hinder economic and social development and also has a negative impact on the environment. A simple mathematical model is used to analyze the different types of road intersections in terms of their Performance in relation to managing traffic congestion and to establish the condition for stability of the road intersections after sufficiently longer periods of time (steady-state). In the analysis, single and double lane un-signalized, signalized and roundabout intersections are evaluated on the basis of their performance (expected number of vehicles and waiting time). Experimental scenarios are carefully designed to analyze the performance of the different types of intersections. It is noted that under light traffic, roundabout intersections perform better than unsignalized and signalized in terms of easing congestion. However under heavy traffic, signalized intersection perform better in terms of easing traffic congestion compared to un-signalized and roundabout intersections. It is further noted that for stability of a road intersection, the proportion of the time a road link stopping at an intersection is delayed should not exceed the utilization factor (the ratio of the arrival rate of vehicles to the product of number of service channels and service rate).
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    Modelling the Use of Insecticide-Treated Cattle to Control Tsetse and Trypanosoma brucei rhodesiense in a Multi-host Population
    (Bulletin of Mathematical biology, 2014) Kajunguri, Damian; Hargrove, John W.; Ouifki, Rachid; Mugisha, J.Y.T.; Coleman, Paul G.; Welburn, Susan C.
    We present a mathematical model for the transmission of Trypanosoma brucei rhodesiense by tsetse vectors to a multi-host population. To control tsetse and T. b. rhodesiense, a proportion, ψ, of cattle (one of the hosts considered in the model) is taken to be kept on treatment with insecticides. Analytical expressions are obtained for the basic reproduction number, R0n in the absence, and RT 0n in the presence of insecticide-treated cattle (ITC). Stability analysis of the disease-free equilibrium was carried out for the case when there is one vertebrate host untreated with insecticide. By considering three vertebrate hosts (cattle, humans and wildlife) the sensitivity analysis was carried out on the basic reproduction number (RT 03) in the absence and presence of ITC. The results show that RT 03 is more sensitive to changes in the tsetse mortality. The model is then used to study the control of tsetse and T. b. rhodesiense in humans through application insecticides to cattle either over the whole-body or to restricted areas of the body known to be favoured tsetse feeding sites. Numerical results show that while both ITC strategies result in decreases in tsetse density and in the incidence of T. b. rhodesiense in humans, the restricted application technique results
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    Threshold And Stability Results For A Malaria Model In A Population With Protective Intervention Among High‐Risk Groups
    (Mathematical Modelling and Analysis, 2008) Tumwiine, J.; Mugisha, J.Y.T.; Luboobi, L.S.
    We develop a mathematical model for the dynamics of malaria with a varying population for which new individuals are recruited through immigration and births. In the model, we assume that non-immune travellers move to endemic regions with sprays, smear themselves with jelly that is repellent to mosquitoes on arrival in malarious regions, others take long term antimalarials, and pregnant women and infants receive full treatment doses at intervals even when they are not sick from malaria (commonly referred to as intermittent preventive therapy). We introduce more features that describe the dynamics of the disease for the control strategies that protect the above vulnerable groups. The model analysis is done and equilibrium points are analyzed to establish their local and global stability. The threshold of the disease, the control reproduction number, is established for which the disease can be eliminated.