The control of vector-borne disease epidemics.

The theoretical underpinning of our struggle with vector-borne disease, and still our strongest tool, remains the basic reproduction number, R(0), the measure of long term endemicity. Despite its widespread application, R(0) does not address the dynamics of epidemics in a model that has an endemic equilibrium. We use the concept of reactivity to derive a threshold index for epidemicity, E(0), which gives the maximum number of new infections produced by an infective individual at a disease free equilibrium. This index describes the transitory behavior of disease following a temporary perturbation in prevalence. We demonstrate that if the threshold for epidemicity is surpassed, then an epidemic peak can occur, that is, prevalence can increase further, even when the disease is not endemic and so dies out. The relative influence of parameters on E(0) and R(0) may differ and lead to different strategies for control. We apply this new threshold index for epidemicity to models of vector-borne disease because these models have a long history of mathematical analysis and application. We find that both the transmission efficiency from hosts to vectors and the vector-host ratio may have a stronger effect on epidemicity than endemicity. The duration of the extrinsic incubation period required by the pathogen to transform an infected vector to an infectious vector, however, may have a stronger effect on endemicity than epidemicity. We use the index E(0) to examine how vector behavior affects epidemicity. We find that parasite modified behavior, feeding bias by vectors for infected hosts, and heterogeneous host attractiveness contribute significantly to transitory epidemics. We anticipate that the epidemicity index will lead to a reevaluation of control strategies for vector-borne disease and be applicable to other disease transmission models.