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