# Inference for epidemics on networks

## Related Staff:

One of the most basic models we have for describing the spread of a disease is the SIR model. The SIR model splits a population into three groups: (S)usceptible, (I)infected and (R)ecovered. One question we might want to ask is, given we know how many people were infected over the course of an epidemic what is an estimate of the rate of infection ($\beta$)? For the SIR model, this can be achieved quite easily. However, one unrealistic assumption of the SIR model is that each individual in a population is equally likely to have an ‘interaction’ with every other individual. That is, if a person is infected then they are equally likely to infect any of the susceptible individuals in the population. Our work aims to remove this assumption from the SIR model by considering a network structure.

One network structure we consider is the Erdos-Renyi network. The Erdos-Renyi network is perhaps the simplest network structure. It places nodes (representing people) uniformly on a unit square, and then places edges between these nodes (representing a possible path of infection) with probability $p$. Now when we consider an epidemic on a network, we will take our infected node(s) and look to see which susceptible nodes they share an edge with, i.e., if a susceptible does not share an edge with any of the infected nodes then that susceptible cannot be infected. Our approach to estimating the rate of infection is to take the final epidemic size as well as some properties/summary statistics of the network and build a linear model that can be used to estimate the rate of infection.

Associated staff: Student — Brock Hermans; Other — Dr Jono Tuke

Inference for epidemics on networks results_p_0pt5