[Back]

A. Böhm, N. Stilianakis, A. Widder:
"Optimal Control of Infectious Diseases in a Population with Heterogeneous Dynamic Immunity";
Report No. 2016-06, 2016; 18 pages.

Exposure to infectious agents triggers immune responses in individual hosts. Heterogeneity of immune responses of the individual hosts and the host population a ects the transmission dynamics of the infectious agent. We extend a previously developed epidemiological modelling approach where heterogeneity of individual-speci c immunity was incorporated and explore optimal control problems associated with the corresponding control strategies. This allows for the study of dynamic interven-
tion scenarios. We focus on vaccination leading to perfect or imperfect immunity as well as treatment and/or chemoprophylaxis interventions depending on the modelling scenario. The objective of the control strategy we explore within the context of an epidemic is to minimise the number of infected individuals and medical costs. We investigate steady states, bifurcation points and make connections
to known properties of simple homogeneous SI-models with respect to critical vaccination thresholds.
Analytical results show that the number of infected persons in an endemic steady state is predominantly determined by the dynamics of immunity. Our ndings show that the level of vaccination
needed to protect the population against an epidemic is similar to that of homogeneous models. For imperfect vaccines the critical vaccination threshold is higher. The versatility of our model can be
shown when combining the cases where vaccination grants immunity for some and partial protection by immune boosting for others. The use of chemoprophylaxis and treatment has the strongest e ect
when chemoprophylaxis is used for the susceptible population early on and widely. The incorporation of population immunity heterogeneities in epidemic modelling shows how immune response can in uence the dynamics of epidemics and can provide insight into the within host and host population
interactions.

mathematical epidemiology, heterogeneous SI-models, optimal control, size-structured systems, immunoepidemiology, treatment, vaccination

http://publik.tuwien.ac.at/files/publik_255140.pdf