Analytic calculation of finite-population reproductive numbers for direct- and vector-transmitted diseases with homogeneous mixing.
The basic reproductive number, R0, provides a foundation for evaluating how various factors affect the incidence of infectious diseases. Recently, it has been suggested that, particularly for vector-transmitted diseases, R0 should be modified to account for the effects of finite host population within a single disease transmission generation. Here, we use a transmission factor approach to calculate such "finite-population reproductive numbers," under the assumption of homogeneous mixing, for both vector-borne and directly transmitted diseases. In the case of vector-borne diseases, we estimate finite-population reproductive numbers for both host-to-host and vector-to-vector generations, assuming that the vector population is effectively infinite. We find simple, interpretable formulas for all three of these quantities. In the direct case, we find that finite-population reproductive numbers diverge from R0 before R0 reaches half of the population size. In the vector-transmitted case, we find that the host-to-host number diverges at even lower values of R0, while the vector-to-vector number diverges very little over realistic parameter ranges.
Department of Biology, McMaster University, Hamilton, ON, Canada, keeganlt@mcmaster.ca.
Lindsay
L
Keegan
Jonathan
J
Dushoff
D000818:Animals; D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D003198:Computer Simulation; D004196:Disease Outbreaks; D004199:Disease Vectors; D006801:Humans; D015994:Incidence; D008962:Models, Theoretical; D011156:Population Density