Merge pull request #162 from dd-harp/dev

Updated vignettes

vignettes/heterogeneous_biting.Rmd

@@ -35,7 +35,9 @@ The software deals mainly with the search weights because the denominators are c
 
 ## Blood Feeding Search Weights 
 
-A flexible implementation is handled through the blood feeding model, which includes the the concepts of *blood feeding search weights* and *availability*. The search weights, $\left\{\omega\right\}$, are a measure of how easy it is for mosquitoes to find and blood feed on a host. The total *availability* of humans for blood feeding is:
+A flexible implementation is handled through the blood feeding model, which includes the the concepts of *blood feeding search weights* and *availability*. The search weights, $\left\{\omega\right\}$, are a measure of how easy it is for mosquitoes to find and blood feed on a host. 
+
+We let $H_i$ denote the size of the $i^{th}$ population, where $$H = \sum_i H_i.$$ The total *availability* of humans for blood feeding is:
 
 $$W = \sum_i \omega_i H_i.$$
 Availability is used to compute the overall blood feeding rate for mosquitoes and the human fraction (human blood meals as a fraction of all blood meals). If we assign a biting weight to a stratum, then the fraction of bites received by that stratum is: 
@@ -49,9 +51,7 @@ $$ \frac{\omega_i H_i}W.$$
 
 ## Relative Biting Rates 
 
-If we let $h$ denote the *average* force of infection (FoI) for a population with multiple strata, and $\xi_i$ the frailty term, then the FoI for the $i^{th}$ stratum is $$h_i = \xi_i h;$$ 
-
-We let $H_i$ denote the size of the $i^{th}$ population, where $$H = \sum_i H_i.$$ 
+The relative biting rates are defined at the top. 
 
 The relative biting rates are constrained such that 
 $$\sum_i \xi_i \frac{H_i}H = 1$$ 
@@ -85,7 +85,8 @@ sum(xi*Hi)/H
 
 ## Implementation
 
-In `exDE,` the concept of human *availability* for blood feeding is also modified by time spent, and the algorithms were designed to deal with both changing denominators and changing search weights. Infective bites in a patch are distributed among population strata by taking a stratum's availability divided by the whole. The blood feeding model outputs a vector of dEIR values for each stratum. 
+In `exDE,` the concept of human *availability* for blood feeding is also modified by time spent, and the algorithms were designed to deal with both changing denominators and search weights. In a patch, the available human population is a measure of the search weighted ambient population density.
+The infective bites in each patch are allocated among human population strata by taking a stratum's availability divided by the total availability of all blood hosts. The blood feeding model outputs a vector of dEIR values for each stratum. 
 
-A relative biting rate is an interesting summary statistic, but it not computed as part of the blood feeding model.  
+Relative biting rates are an important concept, and they are sometimes useful to compute, but they are not computed as part of the blood feeding model.  
 

vignettes/heterogeneous_transmission.Rmd

@@ -16,17 +16,20 @@ knitr::opts_chunk$set(
 
 Blood feeding is an interaction among humans and mosquitoes. Parasite transmission is heterogeneous because mosquito populations are spatially heterogeneous and because human behaviors are heterogeneous. Heterogeneous blood feeding and transmission is an important aspect of malaria transmission dynamics and control, and it has been implemented in `exDE` through several related concepts and constructs. 
 
-+ **Mosquito populations** are heterogeneous over space and time. Spatial dynamics in `exDE` are organized around the concept of a *patch.* The adult mosquito populations in each *state* are assumed to be homogeneously distributed within each patch.
++ *Mosquito populations* are heterogeneous over space and time. Spatial dynamics in `exDE` are organized around the concept of a *patch.* The adult mosquito populations in each *state* are assumed to be homogeneously distributed within each patch.
 
-+ **Human populations:** and human behaviors are heterogeneous in ways that affect exposure and transmission. The design of `exDE` makes it possible to *sub-divide* the human population into an arbitrary number of homogeneous strata. 
++ *Human populations:* and human behaviors are heterogeneous in ways that affect exposure and transmission. The design of `exDE` makes it possible to *sub-divide* the human population into an arbitrary number of homogeneous strata. 
 
-Heterogeneous transmission includes at least three distinct concepts:
++ *Blood feeding* is an interaction between mosquitoes and humans that gives rise to parasite transmission. The design of `exDE` has a new model for blood feeding that incorporates various kinds of heterogeneous transmission. 
 
-+ **[Heterogeneous Biting](heterogeneous_biting.html)**
+Heterogeneous transmission includes several concepts:
 
-+ **[Environmental Heterogeneity](environmental_heterogeneity.html)**
++ **[Heterogeneous Biting](heterogeneous_biting.html)** describes differences among population strata in the average rate of exposure. In effect, heterogeneous biting is a kind of *frailty.* Heterogeneous biting is implemented through *blood feeding search weights.*
 
-+ **[Heterogeneous Mixing](heterogeneous_mixing.html)**
++ **[Environmental Heterogeneity](environmental_heterogeneity.html)** describes the distribution of the expected number of bites in a homogenous populations stratum. For example, if the expected number of bites is *Gamma* distributed, then the number of bites, per person, would have a negative binomial distribution. Environmental heterogeneity is implemented through a function `F_foi` that converts the daily entomological inoculation rate into a daily force of infection (in `Exposure`). 
 
++ **[Heterogeneous Mixing](heterogeneous_mixing.html)** describes departures in a model from the idealized *mass-action* assumption for two-species mixing. The algorithms in `exDE` compute the mixing matrix, $\beta$ integrates information about time spent, mosquito daily activity patterns, the sizes of various population strata, search weights, other vertebrate hosts, and visitors. 
+
++ Temporal variability in mosquito populations driven by exogenous factors, such as weather and vector control,  that modify *potential transmission* by mosquito populations, including **seasonality** and long-term trends.