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

SIS model (page 39)

Numerous infectious diseases confer no long-lasting immunity, such as rotaviruses, sexually transmitted infections, and many bacterial infections. For these diseases, a individuals can be infected multiple times throughout their lives, with no apparent immunity. Here, we concentrate briefly on this class of models, called SIS because recovery from infection is followed by an instant return to the susceptible pool.
By far the most common use of the SIS model  is to capture the dynamics of sexually transmitted infections. Even without births, this set of equations has an endemic equilibrium as recoverying individuals replenish the pool of susceptibles.
We note that S+I =1, so in practise the S equation is redundant.

β is the transmission rate and incorporates the encounter rate between susceptible and infectious individuals together with the probability of transmission.
γ is called the removal or recovery rate, though often we are more interested in its reciprocal (1/γ) which determines the average infectious period.
I(0) is the initial proportion of the population that are infectious.
All rates are specified in days.

All parameters must be positive, and I(0) ≤ 1. Note that S=1-I

C++ ProgramPython ProgramFortran ProgramParametersMATLAB Code.

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