Compartmentalizing an SIR Model of n Susceptibility Classes
Taliha Nadeem · SIAM Undergraduate Research Online · 2016
The purpose of this research is to provide a solution to regulate environmental diseases when the spread of the disease is partly based on how susceptible different groups of individuals are.This study will monitor the effects a disease has on a population with groups of different susceptibility through the administration of vaccines: a point vaccination scheme (PVS) and an interval vaccination scheme (IVS).A PVS entails the instantaneous vaccination of individuals by selectively distributing vaccinations at one point in time, while an IVS is a more realistic vaccination method administered over an interval of time.Both schemes are exclusively administered to individuals classified as having the highest susceptibility to disease.The disease itself will be explored through the use of an 𝑆𝐼𝑅 model of 𝑛 susceptibility classes, a model which studies a disease in relation to susceptible, infected, and removed individuals.To further study the disease, this same model will be modified through the incorporation of differential delay equations, denoting a regaining of susceptibility.These incorporations surface as a reflection of reality: in several diseases, it has been observed that vaccinated individuals or individuals with immunity to the original strain of a disease can regain susceptibility to a mutated strain, such as the common flu whose strains undergo constant mutation.Modification of the disease allows for recovering individuals to contract a viral variant.