Qualitative Behaviour of an Integral Equation Related to Some Epidemic Model

Abstract

Abstract. Sufficient conditions for the uniqueness, global existence and for the convergence to zero when t -> oo of solutions of an integral equation related to an epidemic model are proved. The existence result is proved by applying the Banach fixed point theorem and for the proof of the convergence result a new type of integral inequality is used. IntroductionG. Gripenberg studied in the paper [3] the qualitative behaviour of solutions of the equationwhich arises in the study of the spread of an infectious disease that does not induce the permanent immunity. The existence of a nonnegative, continuous and bounded solution of the equation (1)

Some Fixed Point Results in Spaces with Perturbed Metrics

“…under certain hypotheses about functions g i , K i , i = 1, 2. We note that some particular cases of the equation (3.30) were considered by Griepenberg [3] and Brestovanska [1] to investigate the spread of an infectious disease.…”

Global Existence of Solutions to a System of Integral Equations Related to an Epidemic Model

“…Using the comparison method and some integral estimates, Pachpatte [5] established the convergence of solutions to (1) to 0 as t ⟶ ∞. In [6], Brestovanská studied the integral equation…”

Solvability of a fractional functional equation arising in some epidemic models

“…For more details about the meanings of the various parameters appearing in (1.1), we refer to [6]. In [3], using the Banach contraction principle, an existence result was proved for the following generalized Gripenberg's equation…”