The Science And Maths Behind Corona

The Science And Maths Behind Corona

For three months, the entire world is trying to make sense of COVID-19. Keeping track of all the different figures and the technical terms is hard. Let’s find out what they mean and why they are helpful

Basic Reproduction Number 

The “basic reproduction number” means the spreading potential of a virus. It symbolizes the average number of people an infected person will in turn infect. When this number is bigger than one, it means that each infected person can transmit the virus to at least one other person. When the number is less than one, there is a low chance of the infected person passing on the infection, which means that the disease will typically die out on its own.

For controlling and containing the spread of a virus, its reproduction number must be made less than one. 

According to the Robert Koch Institute, the estimated basic reproduction number of SARS-CoV-2 (the virus behind COVID-19) is between 2.4 and 3.3.

Therefore, each infected person infects about two to three other people. 

That means, for bringing the epidemic under control, about two-thirds of all transmissions must be prevented.

There is, currently, no vaccines available and no reliable protection against the virus that has been found. So, it’s expected that 60% to 70% of the population will likely get infected. Only after that will the virus be unable to spread further, as then it will start encountering more infected people than uninfected. 

Incubation period

The average incubation period for SARS-CoV-2 is five to six days, but can vary from one to 14 days.

Contagious period 

The incubation period is just estimation at this stage. At the moment, the assumption is that an infected person passes on the virus 24 to 48 hours before showing symptoms. Research has suggested that a quarter of all infections are transmitted by people who have yet to show symptoms.

Once an infected person shows symptoms, they become contagious for seven to 12 days if the disease is mild and for more than two weeks if it is severe. The virus is transmitted through droplets. The deeper in the lungs they come from, the longer the virus remains active — imagine it as mucus being more powerful than saliva. By the current evidence, transmitting the virus via excretions is unlikely. 

Case fatality rate

The case fatality ratio is the ratio indicating the risk of death for a person infected with SARS-CoV-2. However, it’s not easy to calculate this risk for the current pandemic.

It can be assumed that there are many cases that are either not known or not recorded. Given such data, the proportion of those who have died compared to all those who have fallen ill becomes disproportionately high. 

Exponential growth of a virus

It’s hard for us humans to understand non-linear growth. When we grow, we intuitively think it is going to keep growing: one today, two tomorrow, and 14 in two weeks. But viruses don’t have the same linear growth, they grow exponentially. An infected person infects another person. These two, then, infect two more, and four infected persons infect eight more people and so on. 

Imagine filling a chessboard with grains of rice. Start with A1 and add rice every day. If the growth was linear, the chessboard would be filled with 64 grains after 64 days. If the growth was exponential, after 64 days there would be an incredible 9,223,372,036,854,775,808 grains of rice on the chessboard.

For tracking the spread of a virus, one must look at its doubling speed. At the moment, the virus needs lesser and lesser time to double. As soon as the doubling speed decreases again, humans will still be infected, but the virus will be on the retreat. 

In his book “The Rules of Contagion: Why Things Spread – and Why They Stop”, mathematician Adam Kucharski identifies four parameters that describe the contagion potential of a disease. In English, they form the initial letters D-O-T-S (dots).

Duration: duration of infectivity. The longer someone is ill, the longer they can infect other people. The sooner an infected person is quarantined from others, the lesser chance they have of transmitting the virus to others. 

Opportunity: how much chance does the virus have of travelling from one person to another? This is a variable that tracks our social behavior. According to Kucharski, normally each person has physical contact with other people about five times a day. This number goes down if social distancing is increased.

Transmission probability: how likely is it for the virus to be actually transmitted from one person to another when two people meet? Kucharski and his team say that this likely happens on every third occasion. 

Susceptibility: after transmission of the virus, how likely is a person to get it? Since there aren’t any protective mechanisms currently, no vaccination, no assured immunity, this figure is close to 100%.

All four of these parameters are adjustment criteria for stopping the spread of the virus. Normally, vaccinations are very effective for this purpose. Since there aren’t any at the moment, we can only work with D, O and T — that includes, isolating the sick, maintaining social distance, coughing and sneezing into our elbows, and washing our hands. 

The aim of the measures currently undertaken is “to flatten the curve.” The number of sick cases must not exceed the capacities of health care systems, so that doctors don’t have to decide between which patients to treat and which not to treat.