SIR Epidemic Models from Individual to Population Behavior

People involved in this project:

1) An SIR model (involving a description of contacts)

The classical susceptible-infectious-recovered (SIR) model, originated from the seminal papers of Ross and Hudson in 1916-1917 and the fundamental contributions of Kermack and McKendrick in 1927-1932, describes the transmission of diseases between susceptible and infective individuals and provides the basic framework for almost all later epidemic models, including stochastic epidemic models using Mont´e-Carlo simulations or Individual Based Models (IBM). By defining the rules of contacts between susceptible and infective individuals, the rules of transmission of diseases through these contacts, and the time of transmission, we provide detailed comparisons between IBM stochastic simulations of an SIR system and the classical deterministic SIR model. More specifically, we distinguish two types of transmission processes: those initiated by susceptible individuals and those driven by infective individuals. Our analysis and simulations demonstrate that in both cases the IBM converge to the classical SIR model only in some particular situations. In general, the IBM and the classical SIR model are significantly different. Our study reveals that the timing of transmission in a contact at the individual level plays a crucial role in the transmission dynamics of a disease at the population level.

 

Case 1: Transmission driven by susceptible individuals

IBM1 and IBM2 (Click to download the MATLAB codes) 

Some numerical simulations of the IMB compared with ODE models : We observe some differences for both deterministic and stochastic simulations depending on the time of transmission in the contact.

Case 2: Transmission driven by infective individuals

IBM1 and IBM2 (Click to download the MATLAB codes) 

Some numerical simulations of the IMB compared with ODE models :  We observe some differences for both deterministic and stochastic simulations depending on the time of transmission in the contact.

 

Publication: