< Modelization

Can we predict the evolution of COVID-19 ?

Text updated on 2020-06-19

It is possible to simulate the COVID-19 epidemic using mathematical models. These models are very useful for assessing the status of the epidemic at a given point in time and forecasting its short-term evolution. In the longer term, they make it possible to envision different potential scenarios for the evolution of the epidemic and to prepare for them.

Mathematical models

To try to predict the course of the COVID-19 epidemic, epidemiologists use mathematical models that simulate the spread of the SARS-CoV-2 virus within a population. Models often incorporate many parameters such as the number of people infected by an infected person, the duration of the infectious phase, the age of infected persons, physical contact, mobility of persons, etc. Not all of these parameters can be determined reliably and may vary from region to region and over time.

A reference model is the "Susceptible Infected Recovered" or "SIR" model developed by Kermack and McKendrick in 1927 to model the dynamics of an infectious disease epidemic in a large population. In this model, individuals in the population are divided into three categories: Susceptible, Infected, Restored. Individuals move between these three categories. From this model, several extensions have been developed to account for exposure, infection, contagion, and immunity.

Initial phase of the epidemic

These models show that in the absence of measures to contain the spread of the SARS-CoV-2 coronavirus in a population, the COVID-19 epidemic results in a significant number of severe cases, far exceeding the hospital resuscitation capacity of most developed countries. These prospects have led the majority of countries to put in place containment measures to prevent or limit the spread of the virus. The rate of attack and the speed of spread depend on population density as well as the age of the population, which explains why the strictest rules have been imposed in the densest metropolises and in the oldest communities.

Second wave(s)

Long-term simulations indicate that the epidemic can rebound after being contained. Epidemic rebounds have already been observed in some early-affected countries (e.g., Saudi Arabia, Iran, Korea, China). These "second waves" are difficult to predict because they depend on parameters that are often difficult to assess or unknown, such as the proportion of the population already infected with the coronavirus, the maintenance of physical distancing measures and barrier gestures, the ability of countries to detect and isolate new cases, the behaviour of individuals, and the duration of immunity.

Effect of the season

The seasonality of the is COVID-19 not yet known. It is likely that, like many infectious respiratory diseases, COVID-19 is slowed during the summer in temperate regions. Although high temperatures and sunlight reduce the transmission of SARS-CoV-2 coronavirus, its high contagiousness and the overwhelming sensitivity of the global human population could outweigh any climatic effects. Furthermore, models that take into account a decrease in coronavirus infectivity show that a summer break does not mean the end of the epidemic. It is highly likely that the disease will become seasonal or that epidemic peaks will occur intermittently, for example, every two years.

Importance of immunity

Models that take into account the immunity of people who have been infected show that this parameter is critical to the long-term evolution of the epidemic. In the majority of countries today, it is estimated that less than 10% of the population has been infected, which is not yet sufficient to confer group immunity that could prevent the arrival of second waves. If immunity is sustained, the epidemic could disappear. On the other hand, if the immunity falls short, it is possible that COVID-19 could become a recurrent disease like the flu. Data on the immune response to SARS-CoV-1 during the 2003 SARS outbreak suggest intermediate immunity approaching 18 months.

facebook twitter linkedin


Modeling the COVID-19 epidemic shows that it can lead to a saturation of the health system.

Ferguson, N., Laydon, D., Nedjati Gilani, G., Imai, N., Ainslie, K., Baguelin, M., ... & Dighe, A. (2020). Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand.

Analysis of the impact of containment on the COVID-19 epidemic in Europe.

Flaxman, S., Mishra, S., Gandy, A. et al. Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature (2020).

Modeling of the COVID-19 epidemic in Ile-de-France and its evolution after the containment phase.

Di Domenico, L., Pullano, G., Sabbatini, C. E., Boëlle, P. Y., & Colizza, V. (2020). Expected impact of lockdown in Île-de-France and possible exit strategies. medRxiv.

Modeling the effect of seasons on COVID-19.

Baker, R. E., Yang, W., Vecchi, G. A., Metcalf, C. J. E., & Grenfell, B. T. (2020). Susceptible supply limits the role of climate in the early SARS-CoV-2 pandemic. Science.

Multi-year epidemic projections taking into account the effect of seasons and duration of immunity.

Kissler, S. M., Tedijanto, C., Goldstein, E., Grad, Y. H., & Lipsitch, M. (2020). Projecting the transmission dynamics of SARS-CoV-2 through the postpandemic period. Science, 368(6493), 860-868.

The duration of the immune response for SARS-CoV-1 was estimated to be 2 years on average from 176 patients.

Wu L-P, Wang N-C, Chang Y-H, Tian X-Y, Na D-Y, Zhang L-Y, Zheng,L, Lan, T, Wang, LF, and Liang, GD. corresponding authors. Duration of antibody responses after severe acute respiratory syndrome. Emerg Infect Dis [serial on the Internet]. 2007 Oct [date cited].

Description of the SIR reference model.

Kermack WO, McKendrick AG. Contributions to the mathematical theory of epidemics--I. 1927. Bull Math Biol. 1991;53(1-2):33-55. doi: 10.1007/BF02464423.

Further reading

Lethality, mortality, excess mortality, R0, kappa: what are we talking about?

What is cross-protective immunity and can it protect me from COVID-19?

What is the risk of meeting a person COVID in a group, knowing the incidence rate?

How many people are contagious with COVID around me?

Why are the COVID-19 epidemiological data on children difficult to interpret?