A pandemic is an epidemic spread over a huge geographical area. COVID-19 is such pandemic documented after 1918 flu pandemic. In this work, we frame a mathematical epidemic model taking inspiration from the classic SIR model and develop a compartmental model with ten compartments to study the coronavirus dynamics in India and three of its most affected states, namely, Maharashtra, Karnataka, and Tamil Nadu, with inclusion of factors related to face mask efficacy, contact tracing, and testing along with quarantine and isolation. We fit the developed model and estimate optimum values of disease transmission rate, detection rate of undetected asymptomatic, and the same of undetected symptomatic. A sensitivity analysis is presented stressing on the importance of higher face mask usage, rapid testing, and contact tracing for curbing the disease spread. An optimal control analysis is performed with two control parameters to study the increase and decrease of the infected population with and without control. This study suggests that improved and rapid testing will help in identifying more infectives, thereby contributing in the decline of disease transmission rate. Optimal control analysis results on stressing on the importance of abiding by strict usage of face mask and social distancing for drastic decrease in number of infections. Time series behaviour of the symptomatic, asymptomatic, and hospitalized population is studied for a range of parameters, resulting in thorough understanding of significance of different parameters.
COVID-19 has become a deadly pandemic in the recent times claiming millions of lives worldwide in a grievous manner. Most of the countries in the world have limited number of medical resources (hospitals, beds, ventilators, etc.), and in the case of large outbreak, it becomes very difficult to provide treatment to every infected individual. In this study, we propound a mathematical model where we classify the infected into two subcategories—asymptomatic and symptomatic. This model further accounts for the effect of limited medical resource for infected people and using face masks in combating the pandemic. Focusing on these aspects, we analyze the model and exploit the available data for assessing the pattern in three most affected countries, namely USA, India and Brazil. The developed model is calibrated to fit data for these three countries and estimate the transmission rate of symptomatic, asymptomatic individuals. The rate at which the individuals who are quarantined recover is estimated as well. Along with these estimations, a comparative study based on the basic reproduction number estimated for the three countries is presented. Standard methods of sensitivity analysis are performed to analyze the ways in which basic reproduction number is impacted upon due to changes in different parameters of the model. Further, we obtain disease-free equilibrium and endemic equilibrium of the model. It is observed that backward bifurcation occurs if the capacity of treatment is small and bistable equilibria are shown that makes the system more sensitive to the initial conditions. Sufficient conditions for the local asymptomatic stability of the endemic equilibrium and disease-free equilibrium of the system are obtained. The results of this study imply that to curb the severity of the increasing cases of the disease in these countries, effective strategies to control disease spread should be implemented so that the basic reproduction number can be decreased below the threshold value which is certainly less than unity. The use of protective masks in public is shown to be an important preventive measure to lower disease transmission rate. Also, the quantity of medical resources should increase so that every infected person can get better treatment.
Human mobility has played a critical role in the spread of COVID-19. The understanding of mobility helps in getting information on the acceleration or control of the spread of disease. The COVID-19 virus has been spreading among several locations despite all the best efforts related to its isolation. To comprehend this, a multi-patch mathematical model of COVID-19 is proposed and analysed in this work, where-in limited medical resources, quarantining, and inhibitory behaviour of healthy individuals are incorporated into the model. Furthermore, as an example, the impact of mobility in a three-patch model is studied considering the three worst-hit states of India, i.e. Kerala, Maharashtra and Tamil Nadu, as three patches. Key parameters and the basic reproduction number are estimated from the available data. Through results and analyses, it is seen that Kerala has a higher effective contact rate and has the highest prevalence. Moreover, if Kerala is isolated from Maharashtra or Tamil Nadu, the number of active cases will increase in Kerala but reduce in the other two states. Our findings indicate that the number of active cases will decrease in the high prevalence state and increase in the lower prevalence states if the emigration rate is higher than the immigration rate in the high prevalence state. Overall, proper travel restrictions are to be implemented to reduce or control the spread of disease from the high-prevalence state to other states with lower prevalence rates.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.