RISK CDT - Stochastic SIS Epidemic Model with Vaccination

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This is a project within the multi-disciplinary EPSRC and ESRC Centre for Doctoral Training (CDT) on Quantification and Management of Risk & Uncertainty in Complex Systems & Environments, within the Institute for Risk and Uncertainty. The studentship is granted for 4 years and includes, in the first year, a Master in Decision Making under Risk & Uncertainty. The project includes extensive collaboration with prime industry to build an optimal basis for employability.

Epidemiology is the study of the spread of diseases with objective to trace factors that are responsible for or contribute to their occurrence. Controlling infectious disease has been an increasingly complex issue in recent years. In the epidemiology, vaccination enables the vaccinated to acquire a permanent or temporary immunity. When the immunity is temporary, the immunity can be lost after a period of time. In many models, one can assume that the process of losing immunity is in the exponential form. Although the classic deterministic SIS model with vaccination plays a special role in our knowledge, it is worth pointing out that epidemic behaviours are inevitably subjected to environmental noise. Therefore, it is practically and theoretically important to reveal how the noise affects the epidemic models. In this project, we shall investigate the dynamics of a stochastic epidemic model, e.g., the large time behaviour of a solution process of this model described by a stochastic differential equation, and identify an approximate threshold value which can be used to determine the extinction and persistence of the disease only subjected to some reasonable constraints.