Incorporating Immunity into Epidemiological Infectious Disease Models: Bridging Multiple Scales


Emerging and on-going infectious disease outbreaks significantly impact the health and economic stability of a population. Understanding and predicting the course of such outbreaks is challenging due to the variability of individuals, particularly with respect to their levels of protection against various infections. This work will address three infectious diseases of worldwide interest: dengue, malaria and whooping cough. Simple mathematical models have been successful at describing the epidemics of and suggesting intervention strategies for simple infectious disease. More complicated diseases, however, require the development and analysis of more complicated models, particularly linking multiple scales - organismal, temporal, and spatial. The novel models and quantitative tools will provide insight into the reason for observed patterns of outbreaks as well as guide strategies for combating these complicated diseases. This work will provide interdisciplinary training for undergraduate and graduate students, and the results of the work will be disseminated to a broad audience through the development of infectious disease based outreach activities and peer-reviewed publications and seminars. Understanding the role of variable immunity within populations is crucial to accurately determining the dynamics of epidemics and to effectively slowing and stopping their spread. This work includes the development, analysis, and simulation of multi-scale models with variability of the individual host immune response. Detailed within-host immune dynamics will be incorporated into population-level epidemiological models of dengue, malaria and pertussis (whooping cough) to evaluate population-level disease dynamics. The aims of this work are three fold: determine the role of within-host viral and immune variability on epidemiological dynamics of dengue; determine the role of adaptive antigen-specific immunity on malaria prevalence and transmission potential; and develop a model of waning and boosting of immunity to determine optimal primary vaccination and booster dose timing for pertussis. This work furthers the mathematical theory of multi-scale systems of differential equations motivated through the incorporation of within-host heterogeneity in population models. It will build upon mathematical theory from differential equations and non-linear dynamical systems. The main challenge will be analyses of non-linear systems with variable time scales and large dimensionality.


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