A Bayesian Logistic Growth Model for the Spread of COVID-19 in New York

Svetoslav Bliznashki

At the time of writing this note, there is information for the number of infectees three days after the 28 days used in order to fit the model. We used the posterior estimates in order to predict the number of future infectees. More precisely, we used the posterior estimates (including σ) in order to simulate data for future values of t thereby constructing what is known as posterior predictive distributions. For example, for a given future day (e.g. for the 28 th day) we sampled all posterior values for Eq. 2 parameters and for each sample we plugged in the t=28 value in order to obtain a mean prediction value; then we added a random number generated from N(0, σ) where the value for σ is sampled from the posterior alongside the other parameters available for the given step. The resulting predictive distribution has an observed mean, variance, etc. and can be used in order to make point and/or interval predictions (HDIs) as usual. Some results are shown in Table 2 We see that the predictive distributions fail to capture even the immediate true value which once again suggests that indeed the model is inadequate and fails to capture the true trends in the data. Note, however, that the ranges of the prediction intervals increase for later data points which is a desirable quality of a model and is intrinsic to the Bayesian approach employed here. As Fig. 2 (upper right portion) suggests, the model converges too quickly to its upper asymptote and hence its predictions are too low and probably too narrow. This observation is not surprising given that it is well-known that the simple logistic model is applicable only during specific stages of an outbreak and/or when enough data is available (see Wu et al, 2020 for a review). Possible solutions include: improving the model (e.g. Richards, 1959) by adding more parameters which can account better for the deviation of the observed data points from the symmetric S-shaped curve suggested by the logistic growth model; adjusting the prior distributions so as to reflect our expectations of a much higher . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.