The basic reproduction number of plant pathogens: matrix approaches to complex dynamics

The basic reproduction number, R0, is defined as the total number of infections arising from one newly infected individual introduced into a healthy (disease-free) host population. R0 is widely used in ecology and animal and human epidemiology, but has received far less attention in the plant pathology literature. Although the calculation of R0 in simple systems is straightforward, the calculation in complex situations is challenging. A very generic framework exists in the mathematical and biomathematical literature, which is difficult to interpret and apply in specific cases. In this paper we describe a special case of this general framework involving the use of matrix population models. Leading by example, we explain the existing mathematical literature on this subject in such a way that plant pathologists can apply the method for a wide range of pathosystems.