Simple but realistic model of contagion aims for education

Dynamical models can be used to describe aspects of the ongoing pandemic. Giorgio Mantica proposed a fully deterministic dynamical model of the epidemic spreading of disease. The dynamical model is simple enough to train students and sufficiently realistic to simulate real-world phenomena.

Mantica hopes this model of contagion dynamics will be used for educational purposes as well as for research.

“The main aim of this paper is educational,” he said. “It is intended to train graduate students. I hope that my approach will catch their attention.”

This paper is organized to serve as a guide for students with suitable programming skills. Those who do the suggested computer simulations using this model will be introduced to fundamental concepts of dynamical and complex systems, including ergodicity, mixing, and chaos.

By combining features of dynamical systems and complex networks, the model describes the evolution of the health of an individual and the dynamics of a network of people.

In related works, a probabilistic rule is typically implemented to simulate the transmission of infection. However, Mantica developed a deterministic rule so that the health state of each person interacts dynamically, instead of probabilistically, with other people in the network.

The fully deterministic and fairly realistic nature of this system, which was verified with numerical experiments, means it can be used to simulate qualities of a real epidemic, potentially including the ongoing pandemic. Mantica believes the simplicity and flexibility of the model make it a versatile tool for theoretical research.

Source: “Simulating epidemics via the theory of dynamical systems,” by Giorgio Mantica, American Journal of Physics (2022). The article can be accessed at https://doi.org/10.1119/5.0082825 .