Analysis of predator-prey models with infection in both species and human intervention
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Date
2024
Authors
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Journal ISSN
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Publisher
University of Namibia
Abstract
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
Description
A thesis submitted in partial fulfilment of the requirements for the degree of master of science in applied mathematics
Keywords
Predator, Prey, Treatment, Vaccination, Equilibrium points, Eigenvalues, Stability analysis, Jacobian matrix, Routh-Hurwitz criteria