Cholera

http://cph.osu.edu/people/jtien

Cholera SIWR model

Seasonal variations will be used to further improve the model, modeled directly into infection force.

19th centry sample
http://muttermuseum.org/

Haiti, no recorded history of cholera infection. no immune responses.

Cholera spatial spread, waterways, human movement, cell phone movement (Digicel, Flowminder)

Moran's I to compare cell phone movement and cholera spread. Local movement versus waterways.

Community networks with environmental pathogen movement
 patch heterogeneity
 weight directed edges in networks

When can disease invade the network? R0 of the network,

Coupled locations

Next generation matrix (second generation matrix, Diekmann, Heesterbeek, Metz 1990, van den Driessche and Watmough 2002.

Transfer matrix V = Transfer out  - Transfers in + Decay
  Laplacian matrix(from graph theory) can be used model transfer out and in.

   i.e. V = L + D

D = diag{\delta_i}

Time scale have to be right

V^-1 as a perturbation problem

 Langenhop 1971, Laurent series for perturbed singular matrices

According to Tien, lifespan of cholera were fitted with expoential model in the lab. Later, Tien explained that fresh cholera have high infectious rate, so fitness of cholera bacteria has a characteristic of aging.