RCN Marine Disease Modeling and Transmission Workshop

Example solution for multiple species, multiple sub-population model (abalone4)

This model combines model 3a, which has sub-populations, with model 3b, which has multiple species. Details presented in earlier model descriptions are the same as this combined model.

You might be tempted to use this model exclusively in place of earlier models. However, note that this model will fail with only one specie or if there are not at least 2 sub-populations in each direction.

This model looks at multiple species that can be affected by the same pathogen or by a situation where species harbor and release pathogens that affect other species.

For this example, there are two species which release infectious particles which infect the other species. There are differences in infectious rate, reproduction rate and so forth to separate the model responses.

All subpopulations start with 100 susceptibles of species 1 and 50 susceptibles of species 2. The lower left (1,1) subpopulation starts with 1 infected species 1 individual. The circulation is counter clockwise around the outer boxes with no exchange into the two inner boxes (same pattern as model 3a).

model parameters: PAR.Nspecies 2 PAR.Nx 3 PAR.Ny 4 PAR.Uex [0.02 0.02 ; 0 0; 0 0; -0.02 -0.02 ] PAR.Vex [-0.02 0 0.02; -0.02 0 0.02; -0.02 0 0.02] PAR.IPinfect(1) 0.0 0.025 PAR.IPinfect(2) 0.001   0.0 PAR.Iinfect(1) 0.0 0.0 PAR.Iinfect(2) 0.0 0.0 PAR.Dinfect(1) 0.0 0.0 PAR.Dinfect(2) 0.0 0.0 PAR.Imort 0.08 0.08 PAR.Bmort 0 0 PAR.DeadDecay 1.5 1.5 PAR.Irelease 0.01 0.001 PAR.Drelease 0 0 PAR.IPremove 0.001 0.001 PAR.Srepro 0.01 0.01 PAR.Irepro 0.005 0.0 PAR.carry 150 100
Species 2 rapidly is infected by particles released by the single individual of species 1. The second species infectious particles then infects species 1 after a short delay. The infectious particles spread eastward causing a similar infection pattern in the other sub-populations. The populations of species 2 crashes as recruitment is not able to keep up with the disease mortiality.
As the infectious particles from species 1 in the south-western box spreads eastward, species 2 becomes infectied. It then releases infectious particles causing species 1 to become infected. Infected animals die quickly. There influence is removed as quickly.
There are more infectious particles from species 1 because of the higher population and higher particle release. The circulation moves these particles around the domain.