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

Rafal Bogacz

On the basis of data on the number of cases in New Zealand in the period from 25 March to 18 April 2020, we estimated parameters of the model as β = 0.26, γ = 0.42. The lower value of a rate with which individuals become infected β than the rate in which cases are reported γ corresponds to the decreasing number of cases over this period. Table 1 gives estimated probability that the virus has been eradicated in individual DHBs 6 . CC-BY 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (column Pβ). This probability is highly correlated with the number of days with no new cases, also given in Table 1 (r = 0.90, p < 0.01). This relationship is also illustrated in Figure 3 . This relationship is not perfect, for example, the estimate for Whanganui is 44% despite only a single day with no cases, because this most recent case was preceded by 14 days with no cases in this DHB. In agreement with occurrence of cases after such long delays, even the regions without cases for 16 or 17 days have the probability estimate around 90% (rather than 100%). Two most right columns of Table 1 also list the probabilities computed with values of β differing form that estimated (and γ set to preserve the difference between estimated γ and β). These probabilities do not differ much, suggesting that the computation of these probabilities is robust to the biases in parameter estimates ( Figure 2 ).