Abstract
Mathematical formulations for the basic reproduction ratio (R 0) exist for several vector-borne diseases. Generally, these are based on models of one-host, one-vector systems or two-host, one-vector systems. For many vector borne diseases, however, two or more vector species often co-occur and, therefore, there is a need for more complex formulations. Here we derive a two-host, two-vector formulation for the R 0 of bluetongue, a vector-borne infection of ruminants that can have serious economic consequences; since 1998 for example, it has led to the deaths of well over 1 million sheep in Europe alone. We illustrate our results by considering the situation in South Africa, where there are two major hosts (sheep, cattle) and two vector species with differing ecologies and competencies as vectors, for which good data exist. We investigate the effects on R 0 of differences in vector abundance, vector competence and vector host preference between vector species. Our results indicate that R 0 can be underestimated if we assume that there is only one vector transmitting the infection (when there are in fact two or more) and/or vector host preferences are overlooked (unless the preferred host is less beneficial or more abundant). The two-host, one-vector formula provides a good approximation when the level of cross-infection between vector species is very small. As this approaches the level of intraspecies infection, a combination of the two-host, one-vector R 0 for each vector species becomes a better estimate. Otherwise, particularly when the level of cross-infection is high, the two-host, two-vector formula is required for accurate estimation of R 0. Our results are equally relevant to Europe, where at least two vector species, which co-occur in parts of the south, have been implicated in the recent epizootic of bluetongue.
Highlights
Mathematical formulations for the basic reproduction ratio (R0) – defined as the average number of secondary infections produced by a typical primary infection in an otherwise totally susceptible population [1] – exist for several vector-borne diseases including those with one host and one vector, such as malaria [2] and those with two hosts and one vector, such as zoonotic trypanosomiasis [3], African horse sickness [4] and bluetongue [5,6]
For the two-host, two-vector system, we propose to focus on the effects on R0 of varying the ratios of vectors to hosts [linked to vector abundance], the probabilities of transmission from host to vector (b1, b2) [linked to vector competence and temperature-dependent in our model] and the vector host preferences (s1, s2)
Paweska et al [15] demonstrate that, regardless of incubation temperature (10, 15, 18, 23.5 or 30uC), the mean virus titre/midge, infection rate and proportion of infected females with transmission potential (i.e. virus titre/midge $103 TCID50, where TCID50 is the amount of virus that will infect 50% of midges inoculated with it) are significantly higher in C. bolitinos than in C. imicola and suggest that, because of its significantly higher vector competence, C. bolitinos could be the primary vector in areas where it occurs in lower numbers than C. imicola, as well as in these cooler regions
Summary
Mathematical formulations for the basic reproduction ratio (R0) – defined as the average number of secondary infections produced by a typical primary infection in an otherwise totally susceptible population [1] – exist for several vector-borne diseases including those with one host and one vector, such as malaria [2] and those with two hosts and one vector, such as zoonotic trypanosomiasis [3], African horse sickness [4] and bluetongue [5,6]. With the exception of Lopez et al [7], almost no attention has been paid to developing mathematical formulations of R0 where there are both multiple hosts and multiple vectors This is a common situation: for trypanosomiasis in Africa for example, two or more species of tsetse fly vector often co-exist; while for both African horse sickness and bluetongue in southern Africa, two competent vectors (Culicoides imicola and C. bolitinos) are frequently trapped together. Starting in 1999, it was detected in Balkan countries where C. imicola was not known, thereby implicating local Culicoides species, such as the obsoletus and pulicaris groups, as vectors Since these co-occur with C. imicola over the latter’s European range [11], it was reasonable to suspect that they may transmit the virus alongside C. imicola in some places; and epidemiological evidence for this was later provided in Sicily [12]. It is quite likely that two or more vector species have co-transmitted BT virus in several parts of Europe in recent years
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