Epidemiological modeling of infectious diseases and coupling of viral load dynamics

In the following the impacts and importance that mathematics and epidemiological modeling plays on understanding infectious diseases is highlighted. Different methodologies which are used for computationally modeling systems of differential equations are then reviewed in context of being applied to epidemiology. Furthermore, novel methods for ODE systems are highlighted for which dynamics of a virus's variants is coupled with the model in order to investigate the effects the mutations of a virus plays on spreading throughout the population. Variants are a key aspect of viruses which play factors in how they develop and this makes it a viable component to be responsible for how they transport between individuals. Moreover, an epidemiological model for infectious diseases is introduced which has been endowed with viral load dynamics. The proposed model is of hybrid nature with deterministic and stochastic qualities. Unlike the traditional SIR models which are driven by their reproduction number from the infection and recovery rates this model is solely driven on the viral load dynamics of the agents in the population. This unique methodology helps to investigate how the viral load of individuals during the infection period will change the course a virus takes. Mathematical theory for the model and computational results are introduced as well. Overall, epidemiology and mathematics go hand in hand and the relationship they play together for understanding infectious diseases can build more profound understanding about infectious diseases and how to adapt for mitigating the negative effects they can have on a population.