Perturbation of a biological control model of malaria considering species competition
DOI:
https://doi.org/10.17268/sel.mat.2025.02.04Keywords:
Dynamical systems, stability, intraspecific competition, mathematical epidemiologyAbstract
This work studies a mathematical model describing the transmission dynamics of malaria, incorporating intraspecific competition in human and mosquito populations, and biological control through larvivorous fish. We prove the existence of a compact attracting set for the proposed system of differential equations. Through stability analysis, we characterize the disease-free and endemic equilibrium points, determining epidemiologically relevant thresholds. The basic reproduction number (R0) is a key parameter: when R0 ≤ 1, the disease-free equilibrium is globally asymptotically stable, whereas for R0 > 1, a stable endemic equilibrium emerges. Numerical simulations validate the theoretical results and reveal the regulatory effect of intraspecific competition on disease prevalence. Finally, we generalize previous models by incorporating competitive interactions and vector management strategies.
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