Abstract

The dynamics of vector-borne disease transmission track the interplay of environmental, ecological, demographic, and epidemiological factors at various temporal scales. This paper develops a non-linear host-vector compartmental system to describe the dynamics of transmission in the context of environmental seasonality and public health interventions. Human populations of susceptible, exposed, infected, and recovered groups are included in these compartments, as are vector populations of susceptible, exposed, and infected groups as well as larval and adult development phases. Personal protection, larvicides, and adulticides are included as intervention factors, and seasonality is introduced through the periodic transmission mechanism. Positivity, boundedness, feasibility, endemic and disease-free equilibria, threshold property, stability, and sensitivity analysis of the dynamical system's parameters are all examined in the mathematical model. While the Jacobian and Lyapunov approaches provide the qualitative description of the equilibria, the next-generation matrix provides a spectral threshold of the disease dynamics in terms of infection invasion. A numerical scale that links the intensity of interventions with the possibility for transmission is provided by the representation of the composite controls and the efficacy of interventions. In order to establish a mathematical basis for comprehending vector-borne transmission as a coupled biological dynamical system, the theory focuses on the interaction between non-linear transmission, seasonality, vector life cycle structure, and parameter reliance on interventions. In a high-dimensional state space, this theoretical method enables the quantitative examination of biological processes and intervention consequences.