# Predicting the effects of Covid-19 containment measures

A new mathematical model can be used to calculate the impact of mitigation measures against the pandemic

How can we predict the spread of Covid-19? Can containment policies like school closings or social distancing effectively reduce the number of total infections? What are the right measures to keep the number of infections at any given time under a certain threshold to avoid overload of the healthcare system? And how can we optimally distribute a limited number of vaccine units? Applied mathematician Vahid Bokharaie of the Max Planck Institute for Biological Cybernetics in Tübingen developed a mathematical model that is easily adaptable to different countries and circumstances, does not require a lot of data input, and can be implemented with limited computational resources.

Bokharaie’s compartmental model starts from the assumption that each person belongs to one of four groups: the susceptible population (those who have not been infected yet and are at risk of catching the disease), the exposed (those who have been infected but are not contagious yet), the infectious (who are themselves potential spreaders of the disease), and the recovered (who are assumed to have developed immunity after recovering from the disease). Since one important factor for the spread of Covid-19 is the age structure of the population, a realistic model needs to break up each of these compartments – susceptible, exposed, infectious, and recovered – further into age brackets.

But it is not as simple as that: “While the age structure is typically well-known, many other, more elusive parameters come into play as well”, explains Bokharaie: “For instance, one needs to consider how frequent contacts within a given age bracket are, and how much people of different age brackets interact with each other.” Crucial parameters like these may vary between different geographic regions and cultures: in a society where many senior citizens live in nursing homes, Covid-19 will spread differently from how it spreads in a society where caring for the elderly in the family home is the norm. But often reliable data on these factors are not available. It is one of the strengths of Bokharaie’s model that it allows to estimate contact rates and similar parameters from little information – from pandemic data about the spread of the disease which are typically available.

## Containment or immunization? Or both?

According to Bokharaie’s computations, more than nine out of ten Germans would eventually get infected with Covid-19 if the disease were uncontained. Assuming a mortality rate of 0.6 percent, this would mean around 460,000 deaths, equivalent to more than the entire population of Bochum. But maybe even worse, there would be a moment where almost twelve million Germans would be infected at the same time. This would all but guarantee a collapse of the healthcare system, likely resulting in much higher mortality.

So, what is a good containment strategy? Various policies affect different age groups differently, and Bokharaie’s model allows to take that into account. Assuming that closing schools and universities would cut four in five contacts in the age group of people under 20, then despite this rather severe measure, more than four in five Germans would still get catch Covid-19. Self-isolation of the elderly would have a similar effect. Only when combining several measures, one sees a marked decrease in overall contamination: a combination of school closings, self-isolation of the elderly, and social distancing would save almost four in five Germans from an infection.

A complete lockdown (estimated to reduce overall contacts to a tenth of the usual) would push that number even further up, but not by a large margin. It is thus debatable whether the resulting psychological and economic costs of a lockdown would be outweighed. For considerations of this kind, policy makers can use Bokharaie’s model as a basis for evaluating the relative effectiveness of different containment policies. But of course, long-term strategies need to change over time and adapt dynamically to the pandemic situation. Changes of containment policies can be easily included in Bokharaie’s model, so that a variety of possibilities can be simulated within this computational framework.

But what about vaccines? They can be easily incorporated into the model by equating vaccinated individuals with those who were immunized by the disease itself. It is well-known that about two out of three Germans would need to be immunized in order to reach heard immunity. But if one combines vaccinations with a rather lax containment strategy which cuts the frequency of contacts in half, the simulations show that vaccinating just a third of the population would be sufficient!

## A versatile tool for countries with limited resources

Different populations and different pandemic situations require different simulations, and ultimately different measures. “The real strength of the model lies in its versatility,” says Vahid Bokharaie. “It is adaptable to vastly different societies and countries.” The model can even be modified to distinguish between symptomatic and asymptomatic carriers of the virus. All this requires little computational power. Thus, the methodology can be a useful tool for policy makers in different countries, in particular in countries with limited computational resources or with few experts in mathematical epidemiology.