News Release

Brazilian physicists create a model to predict mutations in SARS-CoV-2

The study is published in PLOS ONE. Equations suggest viral population variability can be estimated on the basis of epidemiological data.

Peer-Reviewed Publication

Fundação de Amparo à Pesquisa do Estado de São Paulo

The mutations in SARS-CoV-2

image: Equations suggest viral population variability can be estimated on the basis of epidemiological data view more 

Credit: Marcus de Aguiar

Mutations in SARS-CoV-2 are one of the hottest topics right now. Novel variants of the virus are spreading rapidly in places where the COVID-19 pandemic appeared to have been brought under control and could make the current critical stage last much longer than expected.

A study conducted at the University of Campinas’s Gleb Wataghin Institute of Physics (IFGW-UNICAMP) in the state of São Paulo, Brazil, modeled the mutations undergone by SARS-CoV-2 during replication and the genetic evolution of the virus during the pandemic. The findings are reported in article published in the journal PLOS ONE.

The researchers repeated warnings already proffered by other scientists that the emergence of variants is made more likely when a large proportion of the population has not been vaccinated, owing to slow vaccine rollout or vaccine hesitancy, and that there could be another global surge of cases and deaths if this problem is not urgently addressed.

“Viruses are very simple organisms and cannot reproduce on their own. In order to replicate their RNA, they must use the cells of a host. By damaging the cells, they cause disease. Copying errors are inevitable during the replication process. More complex organisms have error correction mechanisms, but viruses don’t. If any such error gives a virus an advantage in terms of propagation, the mutation becomes important and may end up predominating. If the mutant virus is allowed to spread freely owing to non-vaccination, mutations occur with increasing frequency and tend to spread around the world,” said physicist Marcus de Aguiar, a professor at IFGW-UNICAMP and principal investigator for the study.

Contrary to the claims of denialists, mutations are favored not by vaccination but lack of vaccination, he added. “When a large proportion of the population is vaccinated, the virus stops circulating. Less circulation reduces the viral reproduction rate and the probability that novel variants will appear,” he said.

Traditional epidemiological models focus on numbers of people susceptible, infected, and recovered in a specific period. In this study, the model included a description of the virus’s RNA. “Knowing how different the circulating microorganisms are from the original virus is important to an understanding of the emergence of novel variants,” Aguiar said. “It’s also key to predicting whether someone who has been infected by the original virus can be reinfected by a variant and whether novel variants can escape the action of vaccines designed to combat the original virus.”

As with any scientific model, the model developed in the study is an ideally simplified approximation of what happens in the real world. It is based on the most widely used epidemiological model for infectious diseases, known as SEIR, which stands for Susceptible (individuals who can be infected), Exposed (individuals who are infected but not infectious), Infected (those who can spread the virus by infecting others), and Recovered (those who have recovered from the disease and ideally should no longer be susceptible).

“To avoid excessive complexity, which would make the model mathematically unviable, we assume that individuals classified as ‘recovered’ won’t be infected by any future variant,” Aguiar said. “We also assume mutations are neutral, meaning they don’t give the mutant virus an advantage over the original virus, or a disadvantage, for that matter. That isn’t the case in the real world, but we adopted these simplifications in order to focus on studying the accumulation of viral mutations during the pandemic and how different a virus can become.”

To achieve this objective, the researchers added to the model a description of the virus based on its RNA, with 29,900 nitrogen bases, and a mutation rate of 0.001 per base per year, obtaining the data from the structure and behavior of SARS-CoV-2.

“As long as an individual remains infected, the virus can mutate and be transmitted. We calculated the ‘distance’ between the original virus and the variant from the number of different nitrogen bases in each one. Our equations suggest it’s possible to use epidemiological data [numbers of people susceptible, infected and recovered] to predict the variability of the viral population [the ‘average distance’ between RNA sequences] without needing to have access to a huge amount of genetic data,” Aguiar said.

The researchers tested the model by using the equations and data from the epidemic in China in early 2020 to calculate the “average genetic distance” between the viruses that hypothetically emerged during the period. They compared the results with the distances calculated from locally obtained genetic data for the same period and found the predictions to be a good match with the real-world data.

“When the virus spreads through different communities [cities, countries, etc.], this can lead to very different sequences from the original and increase the likelihood of reinfection, depending strongly on the connectivity between these communities. The less connected two communities are, the greater the difference in the virus that one can transmit to the other. This increases the likelihood that the virus circulating in one of the communities will be able to escape the immune systems of people in the other community,” Aguiar said.

“It’s important to note that in order for the virus to acquire an advantage or disadvantage by mutating, replication defects must occur at specific sites in its RNA. Large genetic distances increase the likelihood of important mutations but don’t guarantee them. Our considerations are based on this perspective.”

The study was supported by FAPESP via a Thematic Project; a Regular Research Grant awarded to Aguiar; and a PhD scholarship awarded to Vitor Marquioni Monteiro, Aguiar’s supervisee and lead author of the article.


About São Paulo Research Foundation (FAPESP)

The São Paulo Research Foundation (FAPESP) is a public institution with the mission of supporting scientific research in all fields of knowledge by awarding scholarships, fellowships and grants to investigators linked with higher education and research institutions in the State of São Paulo, Brazil. FAPESP is aware that the very best research can only be done by working with the best researchers internationally. Therefore, it has established partnerships with funding agencies, higher education, private companies, and research organizations in other countries known for the quality of their research and has been encouraging scientists funded by its grants to further develop their international collaboration. You can learn more about FAPESP at and visit FAPESP news agency at to keep updated with the latest scientific breakthroughs FAPESP helps achieve through its many programs, awards and research centers. You may also subscribe to FAPESP news agency at

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