We combine the Leslie model and its derivatives with the classical compartmental SIRS models to build a model of transmission of infected diseases, in a population of hosts, whether opened or closed systems. We calculate the basic reproductive rate R 0 . Under certain conditions, when 0 < 1, there is a disease-free equilibrium that is locally asymptotically stable. In contrast, when 0 > 1, this equilibrium is unstable. en, through an example, we show how we can de�ne public health strategies to tackle an endemic. �inally we carry a global sensitivity analysis based on this basic reproduction rate to exhibit the most in�uential parameters of our model that are applied to in�uenza.

For a simply connected domain G properly contained in C, we apply the results of [3] and [8] to extend the results of [9] to Bergman spaces of simply connected domains A p (G). As a corollary to these results, we present characterizations of compactness of bounded composition operators on A p (G) and give an example illustrating the main results.

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