Browsing by Author "Massawe, Laurencia Ndelamo"

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    Temporal model for dengue disease with treatment
    (University of Dar es Salaam, 2014) Massawe, Laurencia Ndelamo
    The mathematical model for the dengue fever disease with treatment is formulated and analysed. Comprehensive mathematical techniques are used to analyse the stability of the model. It is found that using linearization method and Lyapunov function the disease-free equilibrium point is locally and globally asymptotically stable respectively if the reproduction number is less than unity. The additive compound matrices approach is used to show that the dengue fever model’s endemic equilibrium is locally asymptotically stable when trace, determinant and determinant of second additive compound matrix of the Jacobian matrix are all negative. Sensitivity indices of to the parameters in the model are calculated. The sensitivity indices reveal that the average daily biting, maturation rate from larvae to adult, transmission probability from human to mosquito, number of larvae per human, transmission probability from mosquito to human and the number of eggs at each deposit per capita, when each one increases keeping other parameters constant increase the value of implying that they increase the endemicity of the disease as they have positive indices. While other parameters, such as average lifespan of humans, natural mortality of larvae, mean viremic period and average lifespan of adult mosquitoes, decrease the value of . Numerical simulations are performed using a set of reasonable parameter values. The results suggest that treatment will have a control of dengue fever disease