ABSTRACT
The world has been facing the biggest virological invasion in the form of Covid-19 pandemic since the beginning of the year 2020. In this paper, we consider a deterministic epidemic model of four compartments based on the health status of the populations of a given country to capture the disease progression. A stochastic extension of the deterministic model is further considered to capture the uncertainty or variation observed in the disease transmissibility. In the case of a deterministic system, the disease-free equilibrium will be globally asymptotically stable if the basic reproduction number is less than unity, otherwise, the disease persists. Using Lyapunov functional methods, we prove that the infected population of the stochastic system tends to zero exponentially almost surely if the basic reproduction number is less than unity. The stochastic system has no interior equilibrium, however, its asymptotic solution is shown to fluctuate around the endemic equilibrium of the deterministic system under some parametric restrictions, implying that the infection persists. A case study with the Covid-19 epidemic data of Spain is presented and various analytical results have been demonstrated. The epidemic curve in Spain clearly shows two waves of infection. The first wave was observed during March-April and the second wave started in the middle of July and not completed yet. A real-time reproduction number has been given to illustrate the epidemiological status of Spain throughout the study period. Estimated cumulative numbers of confirmed and death cases are 1,613,626 and 42,899, respectively, with case fatality rate 2.66% till the deadly virus is eliminated from Spain.
ABSTRACT
The Covid-19 pandemic has put the world under immeasurable stress. There is no specific drug or vaccine till now that can cure the infection or protect people from the infection of coronavirus. It is therefore prudent to use the existing resources and control strategies in an optimal way to contain the virus spread and provide the best possible treatments to the infected individuals. Use of the repurposing drugs along with the non-pharmaceutical intervention strategies may be the right way for fighting against the ongoing pandemic. It is the objective of this work to demonstrate through mathematical modelling and analysis how and to what extent such control strategies can improve the overall Covid-19 epidemic burden. The criteria for disease elimination & persistence were established through the basic reproduction number. A case study with the Indian Covid-19 epidemic data is presented to visualize and illustrate the effects of lockdown, maintaining personal hygiene & safe distancing, and repurposing drugs. It is shown that India can significantly improve the overall Covid-19 epidemic burden through the combined use of NPIs and repurposing drugs though containment of spreading is difficult without serious community participation.