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

SIS model with multiple risk groups (page 64)

As an extension of Program 3.1, we now formulate equations (and programs) for an SIS-type infection in a population that can be structured into multiple risk groups, labelled 1,...,m.  Again we define Ii as the proportion of the entire population that are both infectious and in risk group i, and set ni as the proportion of the population that are in group i irrespective of infectious status.
The dynamics of each risk group is derived from two basic events, infection and recovery, with infection coming from any of the risk groups.   (Note, throughout this book we use the same ordering of subscripts such that transmission is always βto from.) For a general SIS model with any number of risk classes we obtain the following differential equations:

is the number of risk groups.
β is the (m) matrix of transmission rates and incorporates the encounter rate between susceptible and infectious individuals together with the probability of transmission.
γ is a vector of recovery rates, one for each risk group.
n is the vector of proportion of the population that are in each risk group
I(0) is the vector of initial proportions of the population that are both infectious and in each risk group.
All rates are specified in years.

All parameters must be positive, and  ni ≤ 1,  Σni=1, Ii(0)≤ ni. For computational simplicity, we insist that m≤20.
It is also usual for β to be symmetric.

C++ ProgramPython ProgramFortran ProgramParametersMATLAB Code.

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