PhD Theses

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Browsing PhD Theses by Author "Elisamehe, Bright"

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    Modelling and Optimal Control of Insect Transmitted Plant Disease
    (University of Dar es Salaam, 2016) Elisamehe, Bright
    A non-linear mathematical model is formulated and analyzed to study the optimal control of the insects transmitted plants disease. The modelling sub-divided into two sub populations namely the plant population and the insect population. The plant population is divided into two classes, namely: susceptible plants and infected plants and vector(insect) population comprises susceptible vector and infected vector. The rate of disease transmission is from infected vectors to susceptible plants. The quantitative analysis for positivity and boundedness of the solutions are determined sensitivity analysis and the basic reproduction number (R0) are calculated. The existence and stability analysis for the disease-free equilibrium point (DFE) and endemic equilibrium point (EE) are analysed. Ruth Hurwitz criterion is used in the analysis of disease –free equilibrium point (DFE) and it shows that when reproduction number is less than one it is locally asymptotically stable and unstable if reproduction number is greater than one. Endemic equilibrium point analysed by using centre manifold theory which shows that the model behaves in the backward bifurcation at reproduction number equal to one for some parameter values. The optimal control model is formulated and analysed with the intention of minimizing the transmission of disease from infected vector (insect) to susceptible plant, by introducing a plant inoculation for resistance to disease as control. It is concluded that, if the disease will be controlled then more plants will be produced compared with plants without disease control.