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We propose a realistic model for the evolution of the COVID-19 pandemicsubject to the lockdown and quarantine measures, which takes into account thetime-delay for recovery or death processes. The dynamic equations for theentire process are derived by adopting a kinetic-type reaction approach. Morespecifically, the lockdown and the quarantine measures are modelled by somekind of inhibitor reactions where susceptible and infected individuals can betrapped into inactive states. The dynamics for the recovered people is obtainedby accounting people who are only traced back to hospitalised infected people.To get the evolution equation we take inspiration from the Michaelis- Mentenenzyme-substrate reaction model (the so-called MM reaction) where the enzyme isassociated to the available hospital beds, the substrate to the infectedpeople, and the product to the recovered people, respectively. In other words,everything happens as if the hospitals beds act as a catalyser in the hospitalrecovery process. Of course, in our case the reverse MM reactions has no sensein our case and, consequently, the kinetic constant is equal to zero. Finally,the O.D.E.s for people tested positive to COVID-19 is simply modelled by thefollowing kinetic scheme S+I=>2I with I=>R or I=>D, with S, I, R, and Ddenoting the compartments Susceptible, Infected, Recovered, and Deceasedpeople, respectively. The resulting kinetic-type equation} provide the O.D.E.s,for elementary reaction steps, describing the number of the infected people,the total number of the recovered people previously hospitalised, subject tothe lockdown and the quarantine measure, and the total number of deaths. Themodel foresees also the second wave of Infection by Coronavirus. The testscarried out on real data for Belgium, France and Germany confirmed thecorrectness of our model.

Modelling the Spreading of the SARS-CoV-2 in Presence of the Lockdown and Quarantine Measures by a "Kinetic-Type Reactions" Approach