-
Notifications
You must be signed in to change notification settings - Fork 0
/
400-Blood-Feeding-and-Transmission.Rmd
50 lines (24 loc) · 2.57 KB
/
400-Blood-Feeding-and-Transmission.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
# (PART) Transmission {-}
# Blood Feeding and Transmission
The endpoint
### Search and Risk
### 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 [@WuSL2023SpatialDynamics].
+ 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 ($O$).
### 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 $q = W/B$.
### 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;
## Host Availability
## Blood Feeding Rates
## The Human Fraction
## The Mixing Matrix, $\beta$