A SIR epidemic model structured by immunological variables

Standard mathematical models for analyzing the spread of a disease are usually either epidemiological or immunological. The former are mostly ordinary differential equation (ODE)-based models that use classes like susceptibles, recovered, infectives, latently infected, and others to describe the evolution of an epidemic in a population. Some of them also use structure variables, such as size or age. The latter describe the evolution of the immune system/pathogen in the infected host - evolution that usually results in death, recovery or chronic infection. There is valuable insight to be gained from combining these two types of models, as that may lead to a better understanding of the severity of an epidemic. In this article, we propose a new type of model that combines the two by using variables of immunological nature as structure variables for epidemiological models. We prove the well-posedness of the proposed model under some restrictions and conclude with a look at a practical application of the model.