Modelling the influence of progressive social awareness, lockdown and anthropogenic migration on the dynamics of an epid
- PDF / 1,164,303 Bytes
- 10 Pages / 595.276 x 790.866 pts Page_size
- 108 Downloads / 176 Views
Modelling the influence of progressive social awareness, lockdown and anthropogenic migration on the dynamics of an epidemic R. Bhattacharyya1
· Partha Konar1
Received: 29 June 2020 / Revised: 27 August 2020 / Accepted: 12 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The basic Susceptible-Infected-Recovered (SIR) model is extended to include effects of progressive social awareness, lockdowns and anthropogenic migration. It is found that social awareness can effectively contain the spread by lowering the basic reproduction rate R0 . Interestingly, the awareness is found to be more effective in a society which can adopt the awareness faster compared to the one having a slower response. The paper also separates the mortality fraction from the clinically recovered fraction and attempts to model the outcome of lockdowns, in absence and presence of social awareness. It is seen that staggered exits from lockdowns are not only economically beneficial but also helps to curb the infection spread. Moreover, a staggered exit strategy with progressive social awareness is found to be the most efficient intervention. The paper also explores the effects of anthropogenic migration on the dynamics of the epidemic in a two-zone scenario. The calculations yield dissimilar evolution of different fractions in different zones. Such models can be convenient to strategize the division of a large zone into smaller sub-zones for a disproportionate imposition of lockdown, or, an exit from one. Calculations are done with parameters consistent with the SARS-COV-2 pathogen in the Indian context. Keywords Mathematical model · Susceptible-Infected-Recovered (SIR) · Epidemic migration
1 Introduction The mathematical modelling of infectious disease is necessary to understand its spread among a population as the individuals interact among themselves. Additional to various transmission mechanisms and properties of the pathogen, the spread can also be a function of societal properties which can include social habits, travel patterns, social distancing and personal hygiene. The models—stand-alone or combined with statistical techniques—provide insights related to the severity of infection by predicting the number of infected persons, the rate at which they are getting infected and the mortality rate; among others. The information can further be employed to strategize various interventions in advance to contain the spread. For example, in the ongoing COVID19 pandemic [1] in India, interventions in the form
B
Partha Konar [email protected] R. Bhattacharyya [email protected]
1
Physical Research Laboratory, Ahmedabad 380009, Gujarat, India
of early screenings and isolations along with the ultimate lockdown—claimed by WHO to be “timely and toughest” [2]— are implemented. Effective, but mathematically straightforward, are the compartmental models which assign individuals of a population at a particular stage of the epidemic to designated compartments [3]. Governed by ordinary differential equations (ODEs), indivi
Data Loading...
