Dynamical analysis of a vector-borne disease model with control function strategies

This paper introduces a mathematical model that includes four categories of hosts and five categories of vectors. The study investigates three control function strategies: personal protection, larval reduction, and adult mosquito vector reduction. To analyze the stability of the model, disease-free equilibria (DFE) were obtained by setting the adult population to zero, while endemic equilibria (EE) were identified at a fixed value. The basic reproduction number (R₀) was specified, and the necessary equations for its computation were derived to evaluate the stability of the model. The analysis utilizing the Jacobian matrix (JM) revealed that both DFE and EE exhibit stability when the value of R₀<1 and instability when the value of R₀≥ 1 . Furthermore, a Lyapunov function (LF) was formulated to demonstrate the overall stability of these equilibrium locations. The results suggest that the DFE is globally stable for R₀≤ 1 . Furthermore, when R₀>1 , there is a single unstable equilibrium (EE), indicating that the disease persists. The EE is stable under specific parameter conditions. Numerical simulations demonstrate that effectively implementing control functions u₁,~ u₂ , and u₃ substantially reduces the infected human and adult mosquito populations and maintains the basic reproduction number R₀ below 1. Additional simulations reveal that the parameter c plays a critical role in infection growth. Infections increase exponentially when c≤ 0.0006 , whereas the development of infected humans is regulated when $$c>0.0006$$ . The results highlight how crucial it is to combine vector control and treatment tactics with meticulous parameter management to reduce and possibly completely eradicate the disease transmission.