Assessing the Impact of Contact Tracing, Quarantine and Red Zone on the Dynamical Evolution of the Covid-19 Pandemic using the Cellular Automata Approach and the Resulting Mean Field System: A Case study in Mauritius.

A cellular automaton (CA) depicting the dynamics of the Covid-19 pandemic, is set up. Unlike the classic CA models, the present CA is an enhanced version, embodied with contact tracing, quarantine and red zones to model the spread of the Covid-19 pandemic. The incubation and illness periods are assimilated in the CA system. An algorithm is provided to showcase the rules governing the CA, with and without the enactment of red zones. By means of mean field approximation, a nonlinear system of delay differential equations (DDE) illustrating the dynamics of the CA is emanated. The concept of red zones is incorporated in the resulting DDE system, forming a DDE model with red zone. The stability analysis of both systems are performed and their respective reproduction numbers are derived. The effect of contact tracing and vaccination on both reproduction numbers is also investigated. Numerical simulations of both systems are conducted and real time Covid-19 data in Mauritius for the period ranged from 5 March 2021 to 2 September 2021, is employed to validate the model. Our findings reveal that a combination of both contact tracing and vaccination is indispensable to attenuate the reproductive ratio to less than 1. Effective contact tracing, quarantine and red zones have been the key strategies to contain the Covid-19 virus in Mauritius. The present study furnishes valuable perspectives to assist the health authorities in addressing the unprecedented rise of Covid-19 cases.