Browsing by Author "Chilinga, Fatu M"

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    Modelling dynamics of fusarium wilt of cashew plants with control strategies in the south-eastern region of Tanzania
    (The University of Dodoma, 2023) Chilinga, Fatu M
    This research aims to study the Fusarium wilt disease and its effects on crop production in Tanzania, particularly on cashew plants in the south-eastern region. The study proposes four mathematical models to analyse the different aspects of the disease and its impact on crop production. The first model describes the dynamics of the disease in a natural environment, taking into account the interactions between infected and susceptible plants. The second model addresses the impact of decomposed disease-induced dead plants on disease transmission. The third model investigates the effect of increasing farming awareness on the disease's dynamics and transmission. The fourth model examines the optimal control measures that can be implemented to control the spread of the disease and minimise its impact on crop production. The global and local stability was analysed using the Lyapunov function technique and the Routh-Hurwitz stability criterion. The sensitivity analysis was performed using the normalised forward sensitivity index and the Partial Rank Correlation Coefficient (PRCC) method. The optimal control problem was solved using Pontryagin's Maximum Principle. The study showed a very high disease transmission rate between infected and susceptible plants. The decomposed disease-induced dead plants also played a significant role in transmitting the disease by increasing the fungus saturation in the soil. However, increasing farming awareness of the disease tended to lower the disease transmission rate. The optimal control analysis revealed that using a combination of fungicides and advertisement was the most effective way to minimise the infection and the cost of implementing control strategies for farmers.