An adaptive social distancing SIR model for COVID-19 disease spreading and forecasting

Abstract

Recently, various mathematical models have been proposed to model COVID-19 outbreak. These models are an effective tool to study the mechanisms of coronavirus spreading and to predict the future course of COVID-19 disease. They are also used to evaluate strategies to control this pandemic. Generally, SIR compartmental models are appropriate for understanding and predicting the dynamics of infectious diseases like COVID-19. The classical SIR model is initially introduced by Kermack and McKendrick (cf. (Anderson, R. M. 1991. “Discussion: the Kermack–McKendrick Epidemic Threshold Theorem.” Bulletin of Mathematical Biology 53 (1): 3–32; Kermack, W. O., and A. G. McKendrick. 1927. “A Contribution to the Mathematical Theory of Epidemics.” Proceedings of the Royal Society 115 (772): 700–21)) to describe the evolution of the susceptible, infected and recovered compartment. Focused on the impact of public policies designed to contain this pandemic, we develop a new nonlinear SIR epidemic problem modeling the spreading of coronavirus under the effect of a social distancing induced by the government measures to stop coronavirus spreading. To find the parameters adopted for each country (for e.g. Germany, Spain, Italy, France, Algeria and Morocco) we fit the proposed model with respect to the actual real data. We also evaluate the government measures in each country with respect to the evolution of the pandemic. Our numerical simulations can be used to provide an effective tool for predicting the spread of the disease.

Optimal allocation of limited vaccine to minimize the effective reproduction number

“…We illustrate the model with an example of COVID-19. Although COVID-19 may be more accurately modeled with an SEIR model, several studies have used an SIR model for COVID-19 and have obtained a good fit to the data [12] , [23] , [24] , [25] . Further work is needed to extend our analytical approach to more complex compartmental models that can capture more details of disease transmission and progression.…”

A Control Based Mathematical Model for the Evaluation of Intervention Lines in COVID-19 Epidemic Spread: The Italian Case Study

“…Therefore, it is possible to conclude that in this case, the disease-free equilibrium is stable. When the second equilibrium point exists, see condition (20), the point P e 1 becomes unstable.…”

“…The results show how the use of masks decreases the effective transmission rate, especially with other interventions, such as social distancing and hygienic measures. In particular, social distancing and informative campaigns are discussed in [20,21]. The social distancing measure is modelled by means of a nonlinear function influencing the contact rate; numerical simulations show the impact of this specific containment measure on the virus spread.…”

A Hybrid Compartmental Model with a Case Study of COVID-19 in Great Britain and Israel

“…Furthermore, they can be easily modified to introduce additional classes or more complex equations, in order to get a more comprehensive description of the situation. For the COVID-19 outbreak, several extensions of this model have been proposed in literature, taking into consideration, for instance, the presence of a latency period of the virus [4], the adoption of masks [5] and vaccinations campaigns [6], or restrictive measures and human behavior [7].…”