Abstract
A nonlinear and nonlocal reaction-diffusion system of population growth is investigated which allows for consideration of both age-size and spatial effects. The mortality and fertility processes of the population are assumed to be linear to simplify the exposition. Local existence, continuation property, positivity, and global existence are obtained. This theory is applied to some specific reaction-diffusion epidemic model including the SI system, the SIS system with vertical transmission, and the SIR system.
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