Manila residents leave a confined area this Thursday.Aaron Favila / A
P In May 2020, a few after the SARS-CoV-2 global pandemic emerged, Rustom Antia, Ottar Bjornstad and I tried to envision the future in coexistence with the covid. Would we have to face massive deaths from the disease forever? Could a successful vaccination campaign eradicate it? Would it end up being something like the flu, with vaccines updated every year? Although we cannot predict the future, a model of ordinary differential equations has allowed us to understand the underlying principles and qualitative changes in the system. The results were published in the journal Science last month.
One of the keys that determine the evolution of a pandemic is how immunity is generated and maintained. Understanding the interactions between SARS-CoV-2 and the human immune system is crucial, but as this virus has spread in the human population recently, we do not have this information. However, we can study the other six human coronaviruses. Four of them circulate widely and cause mild colds, and two (SARS-CoV-1 and MERS) have never had much spread, but generate more serious diseases.
With this information, we define a set of ordinary differential equations that model the transition of a person, starting from a susceptible and immunologically naive state , becoming infected and contagious, and then recovered, with the possibility of mild reinfection. The main result of the model – considering its structure and body of data, especially the severity of the disease in infected people (differentiated by age) – is that, once primary infections only occur among young children, the disease will tend to be mild .
Based on the observations from this experiment, we can assume that, once people are infected, they have immunity to severe disease for the rest of their lives. However, their immunity to mild infections is lowered, so they can become reinfected and contribute to the transmission of the virus.
The structure of the model is based on data obtained in an experimental study on the reinfection of an endemic coronavirus, strain 229E. Based on the observations from this experiment, we can assume that, once people are infected, they have immunity to severe disease for the rest of their lives. However, their immunity to mild infections is lowered, so they can become reinfected and contribute to the transmission of the virus. To model this, people have to go from a "fully recovered" to a "partially susceptible" state. We also include births, deaths, and ages.
The model uses US data for the age distribution of the population, age-specific death rates, and birth rates. Additionally, we include a measure of the severity of the disease in people infected with SARS-CoV-2 by age. We consider a wide range of parameters that show that our results are qualitatively robust for a biologically reasonable range of parameters. The parameters are the transmission rate (R0), which measures how many people infects, on average, a single person, in a totally susceptible population; the rate of decline in immunity preventing transmission; and transmission in reinfections, which reflects how contagious people are reinfected compared to those infected for the first time.
The main differences compared to other models is that ours incorporates different types of functional immunity, obtained by exposure to the pathogen or a vaccine
The main differences compared to other models is that ours incorporates different types of functional immunity, obtained by exposure to the pathogen or a vaccine. The highest, called sterilizing immunization, could prevent future infections, and we model it with a “refractive period”, after infection, in which the person is totally immune and cannot become ill or contribute to transmission. In many cases, contact with the virus or the vaccine does not generate this type of immunization in the long term, but it does offer protection against the disease.
Our model separates these two aspects of immunity and shows that if the immunity that prevents transmission is rapidly reduced – as indicated by the data on endemic coronaviruses – and the immunity that prevents the disease is strong and long-lasting, SARS-CoV- 2 can become one of the mild flu-causing coronaviruses in a few years. Indeed, once the entire population has been infected or vaccinated, the only immunologically naive people will be young children who, on average, develop covid as a mild flu.
In our model we do not consider viral evolution or the appearance and interactions of new strains, although these are undoubtedly emerging and will affect these dynamics.
However, in our model we do not consider viral evolution or the appearance and interactions of new strains, although these are undoubtedly emerging and will affect these dynamics. It appears that endemic coronaviruses do not show signs of rapid antigenic evolution, although there is evidence of a more gradual antigenic change and some degree of protection created by previous infections with other strains, which is not considered in the model.
This model shows a very possible long-term trajectory for SARS-CoV-2 – and quite optimistic! – considering the epidemiological implications of different time scales in reducing immunization (both blocking transmission and reducing the disease). The model relies on data from endemic coronaviruses to make predictions about SARS-CoV-2, but it also makes predictions for endemic strains: when they emerge and adults become infected for the first time, they can also cause serious illness. For the future of SARS-CoV-2, this model underscores the need to continue measuring relative immunity reduction rates.
Jennie Lavine is a postdoctoral researcher at Emory University (USA)
Café y Teoremas is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share meeting points between mathematics and other social expressions and cultural and remember those who marked its development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems."
Translation, editing and coordination: Ágata A. Timón García-Longoria (ICMAT)
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