In dd-harp/MicroWNV: Discrete time simulation of West Nile virus

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Biting distribution matrix

In MicroWNV the bloodmeal function uses generic interfaces of the human, adult mosquito, and adult bird components to compute quantities used to simulate transmission of pathogens between the species. It is a function (not a method that dispatches) because it enforces mathematical consistency in how transmission is calculated, regardless of the specific models used to implement each component.

The compute_bloodmeal function which implements this is called after any vector control functions have been called but before any update functions which update model components over a time step have been called. Here we describe how the calculation works, and how it is implemented in the code.

Using the generic human interface we calculate the following values:

• W: from compute_W, gives the weighted person time at risk spent at each patch
• H: from compute_H, gives the total population in each strata
• x: from compute_x, gives the net infectiousness from humans in each strata
• wf: from compute_wf, gives the biting weights of each strata
• Psi: from compute_Psi, gives the time at risk matrix

Likewise we use the generic bird interface to calculate:

• WB: from compute_WB, gives the weighted bird time at risk spent at each patch
• B_pop: from compute_B_pop, gives the total bird population in each patch
• xB: from compute_xB, gives the net infectiousness from birds in each patch
• wfB: from compute_wfB, gives the bird biting weights of each patch
• PsiB: from compute_PsiB, gives the bird time at risk matrix

Two biting distribution matrices (from mosquitoes to humans and birds, respectively) are calculated:

\begin{equation} \beta_{H_{n\times p}} = \mbox{diag}(w_{f}) \cdot \Psi \cdot \mbox{diag}(1/W) \ \beta_{B_{p\times p}} = \mbox{diag}(w_{f_{B}}) \cdot \Psi_{B} \cdot \mbox{diag}(1/W_{B}) \ \end{equation}

After these values have been computed we compute $f$, the blood feeding rate, and $q$, the proportion of blood meals on human hosts. These use the generic interface functions compute_f and compute_q, which dispatch on the adult mosquito type.

Finally the transmission terms which each component uses to independently update over a time step are calculated and sent to each component. These are the EIR (entomological inoculation rate) for humans and birds, and $\kappa$, the net infectiousness of blood hosts (humans and birds) to mosquitoes.

\begin{equation} EIR_{H_{n\times 1}} = \beta_{H} \cdot (fqZ) \ EIR_{B_{p\times 1}} = \beta_{B} \cdot (f(1-q)Z) \ \kappa_{p\times 1} = q \cdot \beta_{H}^{\intercal} \cdot xH + (1 - q) \cdot \beta_{B}^{\intercal} \cdot x_{B} B_{pop} \end{equation}

Force of infection

Once the above terms have been computed, most models will use them in a fairly similar way to compute a force of infection term. For the mosquito component, it is given as $\kappa fq$, the per-capita rate of infection in mosquito population. Humans and birds compute $h = b EIR$. While the specific way that each of these terms is computed and how state is updated using these terms may change between models, all models will use or can be modified to take as input these terms.

dd-harp/MicroWNV documentation built on March 19, 2022, 11:38 a.m.