Physics-inspired simulations predict waves in four countries

As a physicist, I am trained to look for patterns in the data. For example, the movement of the smallest particles may appear random, but it contains patterns and symmetry.

The same is true for human movements and interactions. Most humans move between familiar locations (for example, home and work) and, in most cases, can encounter the same individual like a colleague. But, of course, there are also random interactions in our complex modern world. When you move from one place to another, you are more likely to hit a random stranger. Human movements consist of both “regular patterns and random changes.”

Being able to track and predict human movements and interactions is invaluable in studying the spread of infectious diseases. But how do you explain the inherent randomness? Some scientists used German mobile phone data to track the effects of human migration on the COVID-19 epidemic.

But is there an easier approach?

The Washington Post’s March 2020 article gave my colleagues and me ideas. This article sought to explain to readers how social distance can slow the spread of the new coronavirus. The writer generated a simulation using dots of different colors that moved in random directions and kept colliding with each other. The “infected” point (representing a person) hit the “uninfected” point and reported the infection.

The Washington Post simulation studied the epidemic of the disease as a contact process. This is an idea that has been mathematically studied in great detail. The dots also reminded us of the random (Brownian motion) motion and diffusion of gas atoms. This is a well-studied problem in physics, chemistry, and engineering.

Inspired by that article, I sought a way to find useful patterns of apparent randomness in human mobility as a means of studying the epidemic of highly infectious diseases such as COVID-19. The exercise began as an intellectual shift during the blockade. Since then, three peer-reviewed articles have been published. Our model proved to be very accurate when compared to the observations.

In the third article, Professor DP Mahapatra and I studied the more complex aspect of using the Monte Carlo model to predict multiple infectious waves. Results are compared with data reported from four representative countries (India (about 1.4 billion), United States (330 million), South Africa (60 million), Serbia (7 million)). it was done. These showed a reasonable match with the timing of the COVID-19 waves encountered in these different countries.

Game of chance

To build the model, we used what is called a Monte Carlo simulation. It is commonly used not only in physics, but also in various fields such as engineering and finance. The Monte Carlo method, like other casinos, is named after Monaco’s gorgeous gambling destination, where luck-dependent games are common.

What makes Monte Carlo simulations so attractive is that they take into account the existence of random variables or elements, so they can predict a variety of potential outcomes. For example, in gambling, variables include players, dealers, shuffle cards, and the number of players around the table.

In the case of disease epidemics due to contact (or proximity-based) interactions, one random variable is human movement. To illustrate this in the simulation, we used what is known as a “random walk” in probability theory and statistical physics. This process aims to determine the estimated position of a randomly moving subject. Each different result is a snapshot, many of which are combined to form the whole.

Our first paper, published in 2021, studied the impact of mobility restrictions and intervention strategies on controlling the spread of COVID-19. Simulations have shown that the increase in infection numbers within controlled and restricted populations follows a power law rather than the expected exponential growth used in most epidemiological modeling.

Power law scaling has shown that the number of infections (or deaths) within a constrained population increases in proportion to the power of time (in fractions). One of the interesting points from this paper is that the behavior of power law for epidemic growth naturally emerged from the simulation. This increase in power law was observed in early Chinese data and explained using a modified epidemiological model incorporating blockade and other social distance scenarios.

Following this paper, a second publication in December 2021 provided an empirical model for analyzing and accurately predicting incomplete epidemic growth curves following power law scaling.

Evaluation of continuous waves

The extended simulation described in the third paper sought to take into account the impact of mitigation strategies such as blockade, along with recovery and infection rates, in order to investigate multiple waves of infection. By applying the simulation to the recorded and estimated number of infections, we found that the model was very accurate. These simulations suggest the possibility of South Africa’s fifth wave. The results also showed that further work was needed to include reinfection rates in the light of new mutants such as Omicron, which clearly demonstrated their ability to evade previous immunity. The study also showed that the number of continuous waves of COVID-19 infection in any country depends on population density, mixing ratio, and most importantly, the timing and duration of control interventions such as quarantine and blockade. rice field. Interventions such as mask mandates and vaccination were included in this category.

COVID stays here

We continue to tune the simulation model, especially for reinfection from new variants. We have taken two important lessons learned from the simulation. As restrictions are relaxed, the mobility of the most vulnerable members of the population will increase. Reinfection increases as the recovered individual becomes infected with the new variant.

These factors also apply to South Africa, where many people’s lives are returning to “normal.” Our latest model predicts an important fifth wave. This has been confirmed by experts. In our simulation, the number in South Africa is set to increase rapidly from the end of May to the beginning of June. If unabated, this leads to a long crescendo, and this fifth wave peaks only at the end of 2022. Its rise and peak, and other possible subsequent waves, depend on the steps taken to mitigate it.

Our model and ongoing work underscore the growing consensus that COVID-19 is currently in fashion worldwide and will stay here.

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