Often we hear that without social limitations, Covid-19 pandemic will cause X number of deaths in Y country. But have you ever wondered how scientists simulate the evolution of an epidemic? All assumptions are based on elaborated mathematical models. Don’t worry, you won’t see any formula, just the logic behind it. You may think that such predictions are not as relevant as the practical measures taken to prevent the spreading of the disease. Well, you couldn’t be more wrong. Take this example: when researchers at the Imperial College of London predicted that without any social distancing UK might have faced more than 500.000 deaths, the Prime Minister immediately restricted people’s movements. So, even Boris Johnson believes in mathematical models! The same model predicted 2,2 million deaths in the US if no action was taken. 

To build such predictions, a lot of data analysis has to be performed, because the simulation needs comprehensive information to be reliable and analysis of different data leads to different mathematical models.

Epidemic prediction simulation

Let’s see the easiest possible simulation model for an epidemic. It is based on the understanding of how people move among three different stages and how quickly. People are either susceptible (S) to the virus, have become infected (I) and then either recover (R) or die. The R group is supposed to be immune, so it can no longer spread the infection. Everyone has the same chance to get infected, and infected people are all contagious at the same level. 

The simulation model becomes more complicated when it gets closer to the real world. Several parameters are then considered: age, sex, health condition, employment, number of contacts, and so on. Additional information about the society has to be included: population size and density, commuting, the size of social networks and health-care provision. Thanks to this information, the model can build a virtual city, or region, or country and consider movements and interactions of population groups in space and time. 

When drafting such simulation, it is possible to choose between two options: “equation-based” or “agent-based” strategies. The former takes the whole population and then divide it progressively in groups and subgroups of different sizes, to represent the modern society; in the latter each individual follows unique rules. The main difference resides in how many people act in the same way.

Covid-19 spreading simulation 

When working on Covid-19, a lot of the information required by the simulation model is lacking or just a rough estimate, especially about death and recovery rates, infectivity and incubation time. To fulfill the lack of input, hundreds of simulations have been run so far, slightly changing one parameter at the time, to consider all possibilities. Both equation-based and agent-based strategies have been tried, with similar results: targeting the US, a model based on the former strategy conceived 2,18 million deaths, on the latter 2,2. 

Dynamism of the Covid-19 simulations

Because a simulation model is dynamic, it can be updated according to the novel data collected. For example, researchers at the Imperial College of London changed the percentage of infected people in need of intensive care from 15% to 30%. With only 4000 beds in ICU in the UK, the healthcare system would have been overwhelmed according to the updated model, forcing the government to introduce more restrictive rules.

Another parameter that has been progressively increased is the so-called R0 (R zero), a value that represents the infectivity of the virus. In other words, R0 indicates how many people can be infected by one sick person. Initially the value was set to 2-2,6. Then it was increased to 2,4-3,3, and finally to 3-4,7. 

Unknowns of the Covid-19 simulations

One data that researchers can only hypothesize is the number of non-symptomatic infected people. Without this number, it is impossible to estimate accurately the spreading of the disease. Sewage testing could help in this, but the strategy is still under development. 

Another open question is how people will react to forced changes in their habits? Chinese researchers observed that citizens of Wuhan and Shanghai had between seven and nine times fewer daily contacts with other people during the social-distancing measures imposed by the authorities. It is still too early to have information about this in Europe and US. 

A third question mark is represented by the time. For how long will these restrictive conditions be maintained? Ferguson and colleagues estimate that the current limitations will prevent the immediate overwhelming of the hospital-bed capacity in the US, but a second pandemic wave might be expected later this year. Only a comprehensive testing strategy (like it has been done in South Korea) could prevent this, until a vaccine will become available.