The model divides the population into five sub-populations of humans and three vectors. Boundedness, non-negativity, and continuous dependence of solutions on initial data prove their well-posedness. An explicit expression of the basic reproduction number and stability analysis of equilibria offer insights into disease mitigation and persistence. The Disease-Free Equilibrium is globally stable when the basic reproduction number is below 1, while the Endemic Equilibrium is globally stable when it is greater than 1. Sensitivity analysis identifies key mitigation parameters, and bifurcation analysis reveals the bifurcation parameter. Optimal control strategies are identified through the maximum principle, and numerical simulations exemplify the analytical results.
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Kumar et al. (2024) studied this question.
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