A climate-based model for tick life cycle: positive semigroup theory on Cauchy problem approach

The distribution of ticks is essentially determined by the presence of climatic conditions and ecological contexts suitable for their survival and development. We build a model that explicitly takes into account each physiological state through a system of infinite differential equations where tick population density are structured on an infinite discrete set. We suppose that intra stage development process is temperature
dependent (Arrhenius temperatures function) and that larvae hatching and adult mortality are temperature and water vapor deficit dependent. We analysed mathematically the model and have explicit the R0 of the tick population.