SIS Model

Overview

The dynamics of an epidemic that follows an SIS (susceptible - infected -susceptible) model is slightly different. As explained in the respective page, the SIR model assumes that people that are infected by the virus will build antibodies that make them immune to it in the future.

The SIS model, on the other hand, considers a situation where a person can be susceptible to the virus even after recovering from it. This applies to some diseases, such as the common cold and influenza virus. Here is a video explaining how the model works.

If the R0 of a an epidemic that follows an SIS model is larger than 1, it will spread. If it is lower than 1, it will die off.

There is limited evidence to suggest that this will be the case with SARS-CoV-2.

Susceptible (S) = People who do not have the virus but are vulnerable and could catch it.

Infected (I) = People who have the virus and can actively spread it.

R0 = The average number of people who will catch a disease from one contagious person

Beta = Infection Rate

Gamma = Recovery Rate (1/ Avg. Duration of Infection)

The term I denotes the number of people infected on day t, and S denotes the number susceptible on day t, We will assume a total population, N, of 350 million people.

Equilibrium in this model exists when the change in the number of infected individuals in a time period is 0. There is a closed-form equation that we can use to identify what this equilibrium in a given environment.

This shows that fundamentally, the SIS model is driven by the basic reproductive number, R0, which reflects how contagious the disease is. The R0 value is the number of additional infections that are generated by an infected individual. If R0 > 1, the disease will spread until it reaches some equilibrium, otherwise the population will achieve a disease-free state.

Contributors: Michael Lin, Thejas Suvarna, Rocco Pelà

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