The dynamical properties of transmission models
Endemic infectious diseases constantly circulate in human populations, with prevalence fluctuating about a (theoretical and unobserved) time-independent equilibrium. For diseases for which acquired immunity is not lifelong, the classic susceptible–infectious–recovered–susceptible (SIRS) model provides a framework within which to consider temporal trends in the observed epidemiology. However, in some cases (notably pertussis), sustained multiannual fluctuations are observed, whereas the SIRS model is characterized by damped oscillatory dynamics for all biologically meaningful choices of model parameters.
Using a range of techniques in dynamical systems analysis, this project studies the dynamical properties of generalised transmission models, including the SIRWS model in which immunity may be boosted through exposure, exploring the conditions under which sustained oscillatory dynamics, multistability and chaos may be supported. Numerical simulation, bifurcation analysis and steady-state stability analysis are used to study the properties of these systems. Applications to pertussis, measles and other vaccine preventable diseases are explored.
Related Publications:
- Investigating Viral Interference Between Influenza A Virus and Human Respiratory Syncytial Virus in a Ferret Model of Infection
- Periodic solutions in an SIRWS model with immune boosting and cross-immunity
- Vaccination Programs for Endemic Infections: Modelling Real versus Apparent Impacts of Vaccine and Infection Characteristics
- The dynamical consequences of seasonal forcing, immune boosting and demographic change in a model of disease transmission
- Dynamical crises, multistability and the influence of the duration of immunity in a seasonally-forced model of disease transmission
- The influence of increasing life expectancy on the dynamics of SIRS systems with immune boosting