# Coronavirus: The R factor and the four parameters of contagion

The increasingly popular reproductive factor R, that is, the spread potential of a virus. If the reproduction number is greater than 1, each infected person transmits the disease to at least one other person. Thus, the virus spreads. If the breeding number is less than 1, fewer and fewer people become infected and the number of infected decreases. To contain the spread of a virus, its reproduction number must be less than 1. Mathematically speaking: R <1.

Epidemiologist Adam Kucharski explains what factors play a major role here and works on mathematical models of infectious diseases to better understand its course. Understanding the data can help politicians make decisions to contain the spread of a virus, but it also makes citizens fear for their freedoms.

### Four parameters

Kucharski has experience researching diseases like Ebola, SARS, and the flu, now with COVID-19. In his book *The Rules of Contagion: Why Things Spread – and Why They Stop* (The Rules of Contagion: Why Viruses Spread and Why They Stop) Mentions four parameters that describe the potential for disease transmission. In English, they start with the initials D, O, T, S:

**1. Duration:** It corresponds to the duration of the infection. The longer a person is sick, the longer they can infect other people. The faster you isolate one person from others, the less time you have to pass the virus on to others. The problem with SARS-CoV-2 is that affected people appear to become infected two to three days before symptoms begin. Time when they can infect other people without realizing it.

**2. Opportunity:** How many people does an infected individual have contact with so that the virus can pass to the next? According to Kucharski, under normal circumstances this is, on average, about five times a day. The variable reflects our social behavior. It can be reduced if we increase social distance, for example, by greeting from afar, instead of giving a hug.

**3. Transmission probability:** How likely is the virus to actually spread from one person to another when two people meet? Kucharski and his team assume that this could happen one in three opportunities.

**4. Susceptibility:** Now that we have the time, opportunity, and probability of transmission, how likely is a person to get the virus and get sick? As there is still no vaccine and the infection rate (and with it the rate of potential immune cells) is quite low, this variable is close to 100%. With increased immunization it will decrease. However, it is likely that it can only be significantly reduced with a comprehensive vaccine.

### Reference for political decisions

The rest are mathematics: doing the multiplication with points D, O, T and S gives the reproduction number. The four parameters are the pillars to stop the spread of the virus. Vaccines are normally effective for this purpose. But since these do not exist at the moment, you can only work with D, O and T: isolating the sick, avoiding social contacts, coughing in the arm or washing hands.

The effective reproduction number R must be distinguished from the basic reproduction number Ro. While R indicates how many people are infected, on average, after taking containment measures or a part of the population is immune, Ro describes how many people are infected by an infected person without containment measures. So, R0 assumes that no one has been vaccinated, no one had the disease, and is therefore immune and that there is no way to stop the spread.

The German virology institute Robert Koch assumes that the basic reproduction rate of SARS-CoV-2 is between 2.4 and 3.3. Without containment measures, each infected person would therefore infect two or three other people. In other words, to control the epidemic (that is, R <1), about two thirds of all possible infections should be avoided.

Currently applied measures aim to "flatten the curve". The number of cases should not exceed the capacity of the health systems. So that doctors do not have to face the difficult decision about which patients to attend, and who not.

*Source: DW*