Estimates of Solutions for Integro-Differential Equations in Epidemiological Modeling

Integro-differential equations (IDE) have been applied in a variety of areas of research, including epidemiology. Recently, IDE systems were applied to study dengue fever transmission dynamics at the population level. In this study, we extend the approach presented in a previous study for describing the epidemiological model of dengue fever. In this paper, we find the exact solutions of the corresponding linearized system model by constructing the Cauchy and Green's matrices. Furthermore, we extend our investigation towards estimating the solutions of a closely related nonlinear system. Given that the coefficients of the model are only known approximately, we address the problem of the stability of a system with uncertain coefficients. Furthermore, we estimate the influence of errors in the coefficient determination on solution behavior.