Invasion,persistence and control in epidemic models for plant pathogens: the effect of host demography

Many epidemiological models for plant disease include host demography to describe changes in the availability of susceptible tissue for infection. We compare the effects of using two commonly used formulations for host growth, one linear and the other nonlinear, upon the outcomes for invasion, persistence and control of pathogens in a widely used, generic model for botanical epidemics. The criterion for invasion, reflected in the basic reproductive number, R₀, is unaffected by host demography: R₀ is simply a function of epidemiological parameters alone. When, however, host growth is intrinsically nonlinear, unexpected results arise for persistence and the control of disease. The endemic level of infection (I_∞) also depends upon R₀. We show, however, that the sensitivity of I_∞ to changes in R₀ > 1 depends upon which underlying epidemiological parameter is changed. Increasing R₀ by shortening the infectious period results in a monotonic increase in I_∞. If, however, an increase in R₀ is driven by increases in transmission rates or by decreases in the decay of free-living inoculum, I_∞ first increases (R₀ < 2), but then decreases (R₀ > 2). This counterintuitive result means that increasing the intensity of control can result in more endemic infection.