Browsing by Author "Charles, Mfano"

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    Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs
    (Heliyon, 2024-06-15) Masanja, Verdiana; Charles, Mfano; Torres, Delfim; Mfinanga, Sayoki; Lyakurwa, GA
    This paper presents a mathematical model to understand how rabies spreads among humans, free-range, and domestic dogs. By analyzing the model, we discovered that there are equilibrium points representing both disease-free and endemic states. We calculated the basic reproduction number, using the next generation matrix method. When , the disease-free equilibrium is globally stable, whereas when , the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. The simulations revealed that the contact rates between the infectious agent and humans, free-range dogs, and domestic dogs, have the most significant impact on rabies transmission. The study also examines how periodic changes in transmission rates affect the disease dynamics, emphasizing the importance of transmission frequency and amplitude on the patterns observed in rabies spread. To reduce disease sensitivity, one should prioritize effective disease control measures that focus on keeping both free-range and domestic dogs indoors. This is a crucial factor in preventing the spread of disease and should be implemented as a primary disease control measure.
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    Modelling optimal control of harvested prey predator system incorporating a prey refuge
    (NM-AIST, 2019-03) Charles, Mfano
    prey-predator interactions have been an important role in the dynamics of species populations. This work presents mathematical model for Modelling Optimal control of Harvested prey- predator system incorporating a prey refuge using deterministic differential equations. This study, develops two harvested prey-predator species, in which both species are affected by over-harvesting, furthermore the predator is affected by prey refuge. The intention is to in- vestigate the impacts of over-harvesting to prey-predator species and suggest control strategies to alleviate the problem of loss of prey-predator species. The analysis of stability of equilib- rium points were done by Jacobian matrix, Global stability analysis is done using Lyapunov function while the analysis of optimal control was done using Pontrygians maximum principle (PMP) and Hamiltonian principle. The control strategy suggested is the creation of reserve ar- eas with restrictions of harvesting. The results obtained from theoretical and numerical analysis of the prey-predator with harvesting without control strategies showed that, harvesting affect the prey-predator species negatively. However, the results obtained from numerical analysis of the prey-predator model with control strategies showed that, the use of control strategy encourage the survival of both species