Mathematical theory of structured population dynamics and its applications to mathematical models for infectious diseases

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We formulated structured population dynamics models for infectious diseases to analyse their mathematical structures, and developed key ideas in mathematical epidemiology as the basic reproduction number and its derivatives. In particular, we have shown the estimation methods of the basic reproduction number and relations between the basic reproduction number and the host population growth based on an age-structured infectious disease dynamics model in a stable population. Moreover, we developed the state-reproduction number theory, by which we cleared the eradication condition by case isolation of symptomatic infecteds. Subsequently, we have shown a new approach to formulate the basic reproduction number and the intrinsic growth rate of infecteds in a heterogeneous environment.