Program 4.3 - Full partial immunity model
This example program is a high dimensional model of the interaction between two infectious disease strains with SEIR-type dynamics. It included both temporary and permanent cross-immunity, infection induced mortality and social quarantining due to convalescence. (A full description is given in section 4.1.5)
Parameters
| βi | is the basic transmission rate for strain i |
| σi | is the rate at which individual move from the exposed to infectious class |
| γi | is the recovery rate for strain i |
| δi | is the rate at which individuals leave the quarantine class |
| ν | is the per captia birth rate |
| μ | is the per capita death rate |
| ρi | is the probability of infection-induced mortality |
| φi | is the co-infection probability |
| ξi | is the temporary immuno-suppression/cross-immunity |
| αi | is the permanent immuno-suppression/cross-immunity |
| ψi | is the differential infection-induced mortality |
| N | is the population size, set equal to 1 |
| S(0) | is the initial proportion susceptible to both strains |
| Ei(0) | is the initial proportion exposed to strain i, but no history of the other strain |
| Ii(0) | is the initial proportion infectious with strain i, but no history of the other strain |
| Ci(0) | is the initial proportion convalescing with strain i, but no history of the other strain |
| Ri(0) | is the initial proportion who have previous experienced infection with strain i |
| R12(0) | is the initial proportion who have previously been infected with both strains |
| εi(0) | is the initial proportion who are exposed to strain i, irrespective of their history with the other strain |
| λi(0) | is the initial force of infections due to strain i |
All rates are specified in days.
Requirements.
All parameters must be positive, ρi, φi and ψi are probabilities and should therefore be between zero and one.
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