41 Blood Feeding and Transmission
The endpoint
41.0.2 Search Weights and Availability
To deal with heterogeneous exposure and many other phenomena, we need a sensible way of segmenting humans into population strata. Stratification makes it possible to deal with population heterogeneity.
A new model of blood feeding is based on a model of blood feeding as the endpoint of a search for a blood host [15].
Each sub-population has a search weight (\(w\)), and the total availability of humans for blood feeding (\(W\)) is the sum of the sizes of the strata weighted by their search weights.
We also consider the availability of alternative vertebrate species for blood feeding (\(O\)).
41.0.3 Functional Response
Mosquito blood feeding rates are computed using a functional response to total availability of vertebrate hosts (\(f = F_f(B)\)).
To compute total availability, we add a scaling parameter on alternative hosts, because mosquito preferences can translate into different patterns of search; total availability is \(B=W + O^\zeta\).
The human fraction is proportional to the relative availability of hosts \(q = W/B\).
41.0.4 Environmental Heterogeneity
The search weights thus translate into a kind of Frailty, which is one component of heterogeneous exposure. Important sources of frailty include bednet use, housing type, and age.
We also want to consider variability in exposure within a stratum – what is the distribution of the expected number of bites over time? We have already discussed frailties, so this is a different kind of heterogeneous exposure that we call Environmental Heterogeneity. This helps us to align models with data: mosquito counts data tend to be described well by negative binomial distributions, so it is likely that the distribution of infectious bites also follows a negative binomial distribution. We introduce a function that translate the EIR into the FoI: \[h=F_h(E)\]
In the Ross-Macdonald model, the underlying assumption is consistent with a Poisson distribution, but we have also derived negative binomial hazard rates. Environmental heterogeneity can arise from two sources:
the aggregated distributions of mosquitoes in micro-habitats, and the redistribution of mosquito populations by wind and weather;
random movements of humans around mosquito micro-habitats that affect their risk in a way that doesn’t tend to change the mean;