Pandemics of Focal Plant Disease: A Model

An analytical model of a pandemic, initiated by a single focus and spreading over a continent, is developed, using foci as the smallest units of disease and fields as the smallest units of host. A few generalizing assumptions lead to a parameter sparse model which may answer general questions on pandemics in a qualitative manner. For pandemic spread of disease during one season a `within-season velocity of pandemic spread', C, is expressed in a set of integral equations. Reduction of inoculum during the off-season is expressed by a `survival ratio' of inoculum, epsilon. The effect of the off-season is a `push-back' of the pandemic front over a distance dh. It will be shown how dh is related to C and epsilon. The mean pandemic spread over successive years is calculated as the `polyetic velocity of pandemic spread', V, which depends on C and the push-back distance. The concept of `pandemic effectiveness' is parameterized. Relations between the two velocities of pandemic spread and several models are studied. Velocities of pandemic spread depend in a limited way on field density represented by the `cropping ratio' zeta. A general conclusion is that eradication and containment of a beginning pandemic becomes more difficult when the pandemic effectiveness of the disease is high, the tail of the spore dispersal probability distribution is long, the the sanitation during the off-season is poor, and the growing or epidemic season is long.