An epidemic forecasting method

Table of contents

Article 1: A method to assess epidemics and make decisions in epidemic prevention and control

Article 2: An epidemic forecasting method

Website updating R_T and other indicators operating since 21/09/2021 at onyx.vn/covid19/

Appendix: Weekly updates of the reproduction number and forecasts for some provinces and cities

An epidemic forecasting method

In this article we address the forecasting problem. Forecasting an epidemic is very hard because many different factors affect the epidemic (R_T). It is roughly like the many different factors affecting GDP in economics. For example, the US CDC uses 26 models from different research groups, then combines them into one model (called an Ensemble) ¹.

In the weekly update article, on the noon of 15/7/2021, since R_T on 14/7 was 1.66 and Directive 16 applied to Ho Chi Minh City, we made the rough prediction that the total detected cases in the 4 days 17/7 to 18/7 would be at least 1.5 times the total detected cases in the 4 days 11/7 to 14/7 in Vietnam. However, R_T did not keep falling but went sideways, and today's data show the above ratio is 1.7 (1.62 if R_T is smoothed). In this article, we present a forecasting method different from the rough method.

First let us briefly discuss the rough method. If R_T does not change in the future, the detected cases in the next n*T days are (when R_T > 1)

(Cases in the latest T days) * R_T * (R_T ⁿ – 1)/( R_T – 1).

This method is fast but not good for long periods (large n). For this reason, we present another method that allows forecasting further ahead. Based on our data — only the number of detected cases per day — and the incubation period property of COVID-19, we choose the simplest model, SEIR. We need to change some things when applying SEIR. The I compartment in SEIR will represent new cases detected within T days, and the E compartment represents undetected cases. Finally, we use multiple SEIR models over consecutive time intervals instead of a single SEIR model (or a SEIR with time-dependent parameters), to accommodate changes in the basic reproduction number. Let t₀ be the starting time, T = 4 days before today (so today is t₀ + 4). We choose t₀ as the starting point because we need data to estimate parameters. The parameters used in the SEIR model are listed in the following table (8 parameters).

Parameter	Value	Reason
N: Total population of Vietnam	98 million	Approximate
E₀: Undetected cases on day t₀	Total detected cases from t₀ +1 to t₀ + 4	This is the period when most of these cases are detected
I₀: Detected cases within T days up to t₀	Total detected cases from t₀ – 3 to t₀
Remove₀: Cases unrelated to the transmission process	1 million	Does not affect the model much
Gamma: Average incubation period	4 days	The average incubation period for the Delta variant is about 4 days
Delta	4 days	T
R_e	Estimate of R_T on day t₀
Beta	Computed from the above parameters

We need R_T to predict future cases. Since predicting R_T is hard, we present several scenarios in the following table.

Name	R_T	Reason
Scenario 1	R_T is estimated by the smoothing curve (smooth spline with spar 0.6).	One way to estimate R_T.
Scenario 2	R_T is constant, estimated by today's value of the smoothing curve.	The bad situation where our epidemic suppression is ineffective, only enough to maintain the current situation.
Scenario 3	R_T decreases linearly from today's estimate (1.62) to 1.1 within 3 weeks (a decrease of 0.025/day).	Based on the lockdown situations in some places around the world, Bac Giang, and Bac Ninh, we consider this an optimistic outlook.

Since the current estimate of R_T is nearly constant, we drop scenario 1. The results of scenario 2 are shown in Figures 1 and 2. In Figure 1, we fail and only maintain R_T at 1.62; the epidemic still peaks after about 3 months then declines. However, the detected cases at the peak will exceed 1 million cases/day. The red curve is new infections. New infections exceed detected cases in the early stage because many new infections have not been detected. This reverses in the future as the number of healthy, uninfected people decreases. Figure 2 is Figure 1 limited to 21 days. In just the next 13 days, the total detected cases already reach nearly 100 thousand (not counting undetected cases). The total detected cases in the next 21 days is 219,771.

The results of scenario 3 are in Figure 3. Although we consider this an optimistic scenario, in just the next 17 days the total detected cases already reach about 100 thousand (not counting undetected cases). The total detected cases in the next 21 days is 165,353.

Details on using compartmental models in general and SEIR in particular for forecasting can be found in the slides attached to the previous article and the references cited therein.

References

1. COVID-19 Forecasts: Cases | CDC. Available at: https://www.cdc.gov/coronavirus/2019-ncov/science/forecasting/forecasts-cases.html. (Accessed: 18th July 2021)

Figure 1. Scenario 2 with R_T = 1.62.

Figure 2. Scenario 2 with R_T = 1.62 in the first 21 days.

(Total detected cases in the next 21 days is 219,771.)

Figure 3. Scenario 3 with R_T decreasing linearly from 1.62 to 1.1 over 21 days (a decrease of 0.025/day)

(After 21 days, nearly catching up with the epidemic at 165k cases — this is the optimistic outlook.)