Can the onset and end of an epidemic be predicted? A SARS-CoV-2 modeling case study

The coronavirus disease 2019 (COVID-19) pandemic is now well into its second wave worldwide. It is important to know when a national outbreak begins and when it may be expected to end, so that public health guidelines and non-pharmaceutical interventions (NPIs) – such as travel restrictions and national or regional lockdowns – are appropriately implemented to minimize their economic damage.

A recent study by researchers in France shows how differences in infection history and viral spread patterns are important factors in predicting the time course of a localized epidemic of SARS-CoV-2.

The team has published a preprint of their findings on the medRxiv* server.

Study: Estimating dates of origin and end of COVID-19 epidemics. Image Credit: bob boz / Shutterstock
Study: Estimating dates of origin and end of COVID-19 epidemics. Image Credit: bob boz / Shutterstock

Any epidemiological prediction or inference is most reliable when buttressed by large numbers, since this compensates for or cancels out the inter-individual differences that are invariably present. Most infectious disease models rely on the deterministic approach, assuming a large initial number of infected hosts cross the ‘outbreak threshold.’ This, of course, is not true at the start and end of an epidemic.

Study aims

The current study examined an outbreak of COVID-19 outside China, so as to allow for the detection of some cases before the reported start, due to importation. Hidden viral spread may also occur before the larger epidemic is observed, as was seen from genome sequencing data obtained in Washington state, USA.

The team also analyzed the period over which strict control measures would be needed to bring the prevalence down to below the required thresholds. This should be estimated, including superspreading events and other sources of heterogeneity, to accurately predict the end of an epidemic.

The pandemic has led to several mathematical models being published, which depend on the basic reproduction number R0, and individual differences. Stochastic modeling is also important to examine what role superspreading events play, and how this affects control measures.

Study models

The original discrete stochastic (DS) model proposed by the current study accounts for individual differences in host transmission on the same day following infection, by using a distributed serial interval rather than a single value. Variability in transmission patterns is also accounted for. The researchers aimed to understand how exactly these factors affected the estimated start and end dates of a national outbreak, taking France as an instance.

The researchers used several different models to test their parameters, in addition to the DS model. This included the non-Markovian SEIRHD model, and a classical deterministic Markovian model.

Origin of the epidemic wave

The researchers found that the median delay from the first imported case to the occurrence of 100 deaths a day was 67 days, indicating that in such a case, 93% of outbreaks would continue spreading until they reached this threshold. The impact of superspreading events was a small reduction in the median delay to 64 days, but about 75% of the simulated outbreaks died out before reaching a point at which 100 deaths occurred in a day.

With the SEIRHD model, the median delay was 63 days, for both the deterministic and the stochastic implementation. As expected, however, this model cannot properly capture the data. A deterministic non-Markovian model also produced the same median delay.

The estimates are not affected significantly by a reduction in serial interval distribution. However, the delay is reduced by eight days if the number of imported cases at the beginning is increased from one to five on the same day, but not if, more realistically, the increase is spread over some days.

The researchers did not find any significant change in the period required for an epidemic to reach a point of 100 deaths per day, either with stochasticity or non-Markovian changes. Superspreading events could introduce a slight delay, as could the number of imported cases at the beginning.

The end of the epidemic

The researchers also found that 95% extinction probability was reached only with at least 7.6 months of lockdown, if superspreading events are ignored. When individual heterogeneity is considered, the period is slightly reduced to 6.9 months. Transmission heterogeneity is a parameter that indicates non-transmission by most infected people.

Rebound risk

Accounting for the period over which a newly infected individual can cause secondary cases, the researchers found that once lockdown is relaxed, the probability of new cases is sharply reduced. Here again, transmission heterogeneity reduces the rebound risk by limiting the number of possible transmissions.

Changing the date of lockdown initiation

The researchers found that advancing the lockdown by one month after the onset of the epidemic wave would reduce the time to extinction by 96 days and 92 days – that is, by almost 50% – without and with transmission heterogeneity, respectively. Thus, the earlier the intervention, the bigger the impact is.

If this was only advanced by two weeks, the time to extinction was 95% likely to be within 188 days, without transmission heterogeneity, and 169 days with it, resulting in a reduction of 41 days of lockdown.

As the restrictions relax following the first 55 days of total lockdown, the estimated periods increase. For instance, the time to extinction increases much less if the lockdown initiation date is February 17, compared to two weeks later or one month later. Since the spread of the epidemic would not be as extensive in this case, the most important period would be the first 55 days of the lockdown.

What are the implications?

The greatest impact of randomness in the model parameters is likely to be at the beginning and end of an epidemic, because of the low prevalence of infection and the effect of stochasticity on viral spread patterns. The study estimates that the first wave of the epidemic began on January 16, which agrees with the data obtained from genomic sequencing. The researchers point out that the latter estimate is also uncertain, and sampling incomplete, in France.

The effect of superspreading was to speed up the initial phase of the epidemic, with the date of origin being January 19, because of the role played by superspreading in triggering persistent outbreaks.

The study confirms that cases may be detectable far in advance of the earliest chain of transmission linked to an epidemic. The ability to estimate the period of lockdown restrictions required for the eradication of the epidemic can also help public health authorities to formulate appropriate policies, and to intervene early.

Finally, it draws attention to the risk of rebound in relation to the period of lockdown. Further studies will help understand the impact of superspreading events in the spread of COVID-19.

*Important Notice

medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Journal reference:
Dr. Liji Thomas

Written by

Dr. Liji Thomas

Dr. Liji Thomas is an OB-GYN, who graduated from the Government Medical College, University of Calicut, Kerala, in 2001. Liji practiced as a full-time consultant in obstetrics/gynecology in a private hospital for a few years following her graduation. She has counseled hundreds of patients facing issues from pregnancy-related problems and infertility, and has been in charge of over 2,000 deliveries, striving always to achieve a normal delivery rather than operative.


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