Browsing by Author "Khoa, Lutopu"

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    Analysis of predator-prey models with infection in both species and human intervention
    (University of Namibia, 2024) Khoa, Lutopu
    The intricate interplay between infectious diseases and predator-prey dynamics holds pivotal significance. Within this context, our focus centres on the impact of human intervention through treatment and vaccination. This study delves into a predator-prey system, categorizing the populations as susceptible, infected with the disease, vaccinated when inoculated against infection, and under treatment post-infection. We formulate four comprehensive mathematical models that illustrate varying levels of human intervention: no intervention, intervention in the prey only, inter vention in the predator only, as well as intervention in both species simultaneously. Mathematical proofs of model positivity are provided. Following the derivation of equilibrium points, we analyse their stability by examining the signs of the eigenvalues from the Jacobian matrix and using the Routh-Hurwitz criteria. To verify our qualitative analysis findings, we conduct simulations using varied parameters in Matlab. We then draw conclusions regarding the impact that human intervention can have on a predator-prey system with infection. Simulation results indicated that without human intervention, predators faced extinction, whereas with treatment and vaccination in either the prey alone or in both predator and prey, the intervention demonstrated a positive effect, preventing the extinction of any species. Therefore, this study concludes that human intervention plays a crucial role in preventing species extinction