Malaria Connectivity
Parasite Flows in Structured Populations
Connectivity describes parasite dispersal between infectious bites. If we traced one parasite gene backwards in time, through a sequence of bites, the parasites would move in mosquitoes between one pair of bites, and they would move in humans between the other. Here, we develop formulas that describe connectivity in meta-population models.
Previous: VC Matrix & HTC matrix
To focus on parasite dispersal, we rewrite the VC matrix and the HTC matrix:
- The VC matrix is the product of the average VC \((V)\) a dispersal matrix \([K_V]\):
\[[V] = V [K_V]\] - The HTC matrix is the product of the average HTC \((D)\) and a dispersal matrix \([K_D]\): \[[D] = D [K_D]\] To compute connectivity, we will use these dispersal matrices. Movement from a mosquito back to a mosquito is: \[[K_D] \cdot [K_V]\] and movement from a mosquito back to a human is: \[[K_V] \cdot [K_D]\] In the general sense, movement is characterized by the matrix, but also by a vector:
alternating betwthrough bites that infect a mosquito and the bites that infect a human, alternating back and forth,
- How are parasites re-distributed in a meta-population after one full parasite generation? The spatial \(R_0,\) called \([R]\) is:
\[[R] = [D] \cdot [V] \mbox{ or } [V] \cdot [D] \]
- If we start with all the infections occurring in a meta-population on a single day, and we traced those parasites back or project forward one full parasite generation, where did they come from?
Let \([D]\) be the HTC matrix and \([V]\) be the VC matrix. We define connectivity as the distribution of infective bites in each patch arising from an infection in each patch.
The number of infections in each patch arising from a single human that is infected in each patch.
The number of infections in each patch arising from a single mosquito that is infected in each patch.
Let \([R] = [V] \cdot [D]\)
