Past and future perspectives on mathematical models of tick-borne pathogens

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex lifecycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their lifecycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper we review models of tick dynamics and summarise the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick borne-pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper we identify gaps in the current knowledge and future modelling approaches