Estimating the probability of New Zealand regions being free from COVID-19 using a stochastic SEIR model

Rafal Bogacz

We considered a stochastic version of Susceptible Exposed Infected Recovered (SEIR) model [2] . It assumes that each individual can be in one of 4 states, and move between as illustrated in Figure 1A . We denote by E t and I t the number of presymptomatic and infectious people on day t, and by ∆E t and ∆I t the number of people becoming presymptomatic or infectious. We do not have data on these variables, so we assume they are hidden to us and we will infer their values. On the other hand, we denote by ∆R t , the number of people being reported as a new case on day t, and we assume that this observed number corresponds to the amount of people moving to state R where they no longer infect others (as they become fully isolated). Thus in the presented model the cases reported correspond to individuals moving to state R rather than I as typically assumed, because we assume that the individuals are more likely to infect others when they are unaware that they have COVID-19, rather than after diagnosis when they become particularly careful. Indeed, James et al. recently wrote that the control measures that specifically target confirmed cases, such as isolation, "could be modelled by a larger reduction in transmission rates for confirmed cases" [3] . Here we for simplicity assume that this transmission rate is reduced to 0.