Mathematical structures for integrals to enhance the applicability of integral equations in modelling disease transmission a preliminary study

Abstract

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Nowadays the world has to deal with a large number of diseases which challenge public. Most of these diseases are preventable based on interventions placed at various levels of the transmission of the disease. One such attempt by modern researchers is to construct mathematical models of disease transmission and find solutions to control these diseases. In the basic context, the rates of change of susceptible, infected and immune populations describe the way of disease transmission regardless of proper quantification of the phenomena associated with accumulations such as history of infection, immune response, burden of the disease and effect of prolonged treatments. In that perspective, this study conveys a feeling for modeling in terms of integrals to cater to the accumulations mentioned above, along with integral equations. The study expresses several possible alterations and refinements to enhance the applicability of integral equations. In three cases, we present an easier way of incorporating an accumulation subject to time lag, manipulating Lebesgue integration instead of Reimann integration to cater to a higher degree of discreteness and structural refinements incorporate the increasing complexity of the phenomena.