New York, April 22 : US scientists have developed a new mathematical model for predicting how epidemics such as Covid-19 spread.

This model not only accounts for individuals' varying biological susceptibility to infection but also their levels of social activity, which naturally change over time.

Using their model, the team showed that a temporary state of collective immunity -- which they termed "transient collective immunity"-- emerged during the early, fast-paced stages of the epidemic.

However, subsequent "waves," or surges in the number of cases, are predicted to appear because of changing social behaviours due to pandemic fatigue or variations in imposed mitigations.

The findings are forthcoming in the journal Proceedings of the National Academy of Sciences.

The concept of herd immunity doesn't apply in practice to Covid.

"People's social activity waxes and wanes, especially due to lockdowns or other mitigations. So, a wave of the epidemic can seem to die away due to mitigation measures when the susceptible or more social groups collectively have been infected--something we termed transient collective immunity," according to Nigel Goldenfeld, Professor at University of Illinois Urbana-Champaign (UIUC).

"But once these measures are relaxed and people's social networks are renewed, another wave can start, as we've seen with states and countries opening up too soon, thinking the worst was behind them,"Goldenfeld added.

"Mitigation measures, such as mask wearing and avoiding large gatherings, should continue until the true herd immunity threshold is achieved through vaccination," said Ahmed Elbanna, Professor at UIUC.

"We can't outsmart this virus by forcing our way to herd immunity through widespread infection because the number of infected people and number hospitalised who may die would be too high," he added.

In the study, the team incorporated time variations in individual social activity into existing epidemiological models. They compressed this model into only three equations, developing a single parameter to capture biological and social sources of heterogeneity.

"We call this parameter the immunity factor, which tells you how much the reproduction number drops as susceptible individuals are removed from the population," explained Maslov.

At the city and state level, the reproduction number was reduced to a larger extent in locations severely impacted by Covid. For example, when the susceptible number dropped by 10 per cent during the early, fast-paced epidemic in NYC and Chicago, the reproduction number fell by 40 to 50 per cent--corresponding to an estimated immunity factor of four to five.

This temporary state of immunity arises because population heterogeneity is not permanent. Any increase in social activity means additional exposure risk. The outcome can be that there is a false impression that the epidemic is over, although there are more waves to come.

Social activity, pandemic fatigue behind new Covid-19 peaks