Mathematical structures for integrals to enhance the applicability of integral equations in modeling disease transmission: A preliminary study

Abstract

Nowadays world have to deal with large number of diseases which are challenging public health. Anyhow these diseases are preventable based on interventions placed on various levels of transmission of the disease. One such attempt by the modern day researchers is to incorporate the disease transmission into a mathematical model and find a solution to control these diseases. In the basic context, rate of change of susceptible, infected and immune population describes the way of disease transmission regardless of proper quantification of phenomena associated with accumulations such as history of infection, immune response, burden of a disease and effect of prolonged treatments. In that perspective this study conveys a feeling for modeling in terms of integrals to cater 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 higher degree of discreteness and structural refinements to incorporate increasing complexity of phenomena.