With escalating urbanization, the environmental, demographic and socio-economic heterogeneity of urban landscapes poses a challenge to mathematical models for the transmission of vector-borne infections. One fundamental but neglected axis of environmental spatial variation within cities corresponds to human density.
Although there are many vector-human coupled models, formulated as extensions of the original Ross-MacDonald equations, none of the formulations consider the human production of vector's breeding sites and therefore the dependency of vector abundance on human population density. This independence is a deep-seated assumption lacking empirical justification that implies a decreasing force of infection with host number. We question the independence assumption, introduce an explicit dependence between host and vector densities through different recruitment functions, and examine their consequences on transmission risk and dynamics, in a modified model formulation. In addition, because variation in human density can co-vary in space with that in temperature, we investigate their joint effect on the reproductive number R0.
Results/Conclusions
With a simple modification of the classical equations for vector-borne infections (SIR for humans and SI for vectors), we show that the effect of human density on the force of infection depends strongly on the form of the relationship between of mosquitoes and human numbers represented by a function V(N). In particular, a dense environment does not necessarily imply a dilution of the per-capita infection rate as expected from the common assumption of independent or linear human-vector recruitment. We obtain that the force of infection increases with population density when recruitment grows sufficiently fast, and has a non-monotonic behavior when recruitment saturates with large human numbers. Interaction of these patterns with seasonality in temperature gives rise to pronounced differences in timing, relative peak sizes, and duration of epidemics. Different forms of the proposed dependency V(N) can explain empirical dengue risk patterns observed in the city of Delhi where socio-economic status impacts upon both human and mosquito densities. Our results demonstrate the importance of considering the link between host and vector abundances, with the possibility that social and environmental characteristics can completely reverse the expected pattern of decreased risk per individual as host density increases.