3  Heterogeneities

An assumption of the classical SIR model is homogeneous mixing. To include heterogeneities, we can pick a characteristic to divide the population into subgroups, where each subgroup shares a similar risk of both contracting AND transmitting infection (Keeling & Rohani, 2011).

• Sexually transmitted infections (STIs): subgroups are based on the number of contacts.

• Childhood diseases (measles, mumps, chickenpox - those with a high \(R_0\)): subgroups are based on the nature of contacts, with those in frequent contact with children being at higher risk.

Adding heterogeneities increases the parameters to estimate, often requiring more biological data. Ideally, line list data of which characteristics .

3.1 WAIFW matrix

3.2 Social contact matrix

Keeling, M. J., & Rohani, P. (2011). Modeling Infectious Diseases in Humans and Animals. Princeton University Press. https://doi.org/10.1515/9781400841035