Susceptible-Infected-Recovered model study using free particle dynamics


  • Fernando Garzón Instituto de Investigación en Ciencias Básicas y Aplicadas, UAEM
  • Olvera Orozco Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Temixco, Morelos
  • Jorge Castro Universidad del Mar Campus Puerto Ángel
  • Aldo Figueroa Centro de Investigación en Ciencias, UAEM



SIR, free particles, particle density, COVID–19


A study on the epidemiologic Susceptible-Infected-Recovered (SIR) model is presented using free particle dynamics. The study is performed using a computational model consisting of randomly allocated particles in a closed domain which are free to move inrandom directions with the ability to collide into each other. The transmission rules for the particle–particle interactions are based on the main viral infection mechanisms, resulting in real–time results of the number of susceptible, infected, and recovered particles within a population of N= 200 particles. The results are qualitatively compared with a differential equation SIR model in terms of the transmission rate β, recovery rate γ, and the basic reproductive number R0, yielding overall good results. The effect of the particle density ρ on R0 is also studied to analyze how an infectious disease spreads over different types of populations. The versatility of the proposed free–particle–dynamics SIR model allows to simulate different scenarios, such as social distancing, commonly referredto as quarantine, no social distancing measures, and a mixture of the former and the latter. It is found that by implementing early relaxation of social distancing measures before the number of infected particles reaches zero, could lead to subsequent outbreaks such as the particular events observed in different countries due to the ongoing COVID–19 health crisis


W. O. Kermack, A. G. McKendrick, G. T.Walker.Proc. R. Soc. Lond. A115. (1927), pp.700–721

C. Alexsandro, G. Sebastian.An AlgebraicSolution for the Kermack-McKendrick Model.(2016)

B. Martin, S. Streipert, F.M. Torres.Nonlin-ear Analysis: Hybrid Systems32. (2019), pp.228–238.

J. H. Cáceres.Revista Cubana de InformáticaMédicaNo. 2. (2007), 3erartículo.

A. Stegeman, A. R. Elbers, J. Smak, M. Jong.Prev. Vet. Med.42(3-4). (1999), pp.219-234

Gorbalenya, A.E., Baker, S.C., Baric, al. The species Severe acute respira-tory syndrome-related coronavirus: classi-fying 2019-nCoV and naming it SARS-CoV-2.Nat Microbiol5, 536–544 (2020).

I. Copper, A. Mondal, C. G. Antonopoulos.Chaos, Solitons and Fractals.139, (2020)110057

O. J. Scherer, Computational physics, 3ra ed.(Springer International Publishing AG 2010,2013, 2017), pp. 312

C. A. Dutra, Smoothed Particle Hydrodynam-ics, 1ra ed. (Springer Nature Switzerland AG,2019), pp. 56-60

B. Muth, M. Müller, P. Eberhard, L. Stefan.Discrete Element Methods 07. (2007), pp. 1-18

T. Yadav, S. K. Saxena.Coronavirus Disease2019 (COVID-19). (2020) pp. 33-42.

S. A. Ansari, S. A. Sattar, V. S. Springthorpe,G. A. Wells, W. Tostowaryk.Applied and En-vironmental Microbiology55 (12)pp. 3113-3118

Neil J. Rowan, John G. Laffey.Science of TheTotal Environment,725(2020), 138532

H. Hu, K. Nigmatulina, P. Eckhoff.Mathe-matical Biosciences 244. (2013), pp. 125-134






14 Other areas in Physics