A climate-based model for tick life cycle: an infinite system of differential equation approach

Abstract

The distribution of ticks is essentially determined by the presence of climatic conditions and ecological contexts suitable for their survival and development. We have developed a general tick biology model to study the major trends due to climate change on tick population dynamics under different climate conditions. We build a model that explicitly takes into account stage into 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 precipitations dependent. We analysed mathematically the model and have explicit the R0 of the tick population. Therefore, we performed a numerical analysis of the model under three different climate conditions (tropical, Mediterranean and subarctic climates) over the short term using climatic data from 1995 to 2005, as well as long-term simulations from 1902 to 2005.