On solvability of one infinite system of nonlinear functional equations in the theory of epidemics

In the present paper, an infinite system of nonlinear functional equations arising in the theory of epidemics is investigated. We prove a constructive theorem on the existence of a nontrivial, continuous and bounded solution of the system. In addition, some asymptotic properties of the constructed solution are studied. We conclude the study by applying our theoretical results to two concrete examples arising in spatial-temporal spread of epidemics and in $p$-adic string theory.