Modeling Infectious Diseases in Humans and Animals
Matt J. Keeling & Pejman Rohani

Full partial immunity model (page 126)

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 convalescance. (A full description is given in section 4.1.5)


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.
is the per captia birth rate
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.
is the initial proportion susceptible to both strains.
is the initial proportion exposed to strain i, but no history of the other strain
is the initial proportion infectious with strain i, but no history of the other strain
is the initial proportion convalescing with strain i, but no history of the other strain
is the initial proportion who have previous experienced infection with strain i
is the initial proportion who have previously been infected with both strains.
is the initial proportion who are exposed to strain i, irrespective of their history with the other strain.
is the initial force of infections due to strain i.
All rates are specified in days.

All parameters must be positive,  ρi, φi and ψi are probabilities and should therefore be between zero and one.


Questions and comments to: or
Princeton University Press
Our research web pages:
Matt Keeling      Pejman Rohani