ABSTRACT
In this study, we estimate the basic reproduction number (R0 ) for the ongoing COVID-19 pandemic for 10 seriously affected states and for the whole country for the lockdown period. For this, we formulate a SEIQHR mathematical model and fitted it to cumulative COVID-19 cases. The Government of India implemented the first phase of nationwide lockdown from March 25, 2020 to April 14, 2020 and extended the same from April 15, 2020 to May 3, 2020. We measure the effectiveness of the nationwide lockdown on the spread of COVID-19 in India. For this, we have estimated the basic reproduction number for three phases;namely March 14–31, 2020 (Phase I), April 1–15, 2020 (Phase II), and April 16–30, 2020 (Phase III). Our study finds that, in all the cases, the value of the R0 is minimum at the end of phase III. This demonstrates the success of the implementation of lockdown in reducing the value of the basic reproduction number. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
Since the start of COVID-19 pandemic, the definition of normal life has changed drastically. The number of cases of this pandemic is rising everyday across the globe. In this study, we propose a compartmental model, which considers the isolation factor of Coronavirus infected individuals. The model consists of five compartments: susceptible (S), exposed (E), Infected (I), Isolated (L) and recovered (R). We have estimated the parameters of the model system and the expression of the basic reproduction number R-0 using real data set. The exact value of the basic reproduction number is computed for India, Brazil and Peru. The local and global stability analysis of disease-free equilibrium and endemic equilibrium points is carried out. The forecasting of the pandemic is done using real data. It has been observed that to understand the pandemic the time frame has to be divided into small intervals as the parameters of the pandemic are changing with time. Within a time frame of approximately four months (i.e. from July to October 2020), the transmission rate of India has been reduced by approximately 84%. Whereas the transmission rate in Brazil and Peru has increased by 79% and 45% respectively. The sensitivity of various parameters involved in the model has been analyzed. We have presented a complete analysis to check the existence of backward bifurcation.
ABSTRACT
Italy faced the COVID-19 crisis in the early stages of the pandemic. In the present study, a SEIR compartment mathematical model has been proposed. The model considers four stages of infection: susceptible(S), exposed (E), infected (I) and recovered (R). Basic reproduction number R0 which estimates the transmission potential of a disease has been calculated by the next-generation matrix technique. We have estimated the model parameters using real data for the Coronavirus transmission. To get a dipper insight into the transmission dynamics, we have also studied four of the most pandemic affected regions of Italy. Basic reproduction number stood differently for different regions of Italy i.e. Lombardia (2.1382), Veneto (1.7512), Emilia Romagna (1.6331), Piemonte (1.9099) and for Italy at 2.0683. The sensitivity of R0 corresponding to various disease transmission parameters has also been demonstrated via numerical simulations. Besides, it has been demonstrated with the help of simulations that earlier lockdown and rapid isolation of infective individuals would have been helpful in a dual way;by substantially reducing the number of susceptible people on one hand and preponing the end of the pandemic on the other. This paper also includes complete theoretical analysis of the proposed model including the epidemic feasibility of the model and existence of endemic equilibrium point. We have also derived the conditions under which the disease became endemic. Since the existence of an endemic equilibrium point refers to the possibility of backward bifurcation, we have given a detailed analysis regarding the same. All the theoretical analysis is supported by detailed numerical simulations to understand the transmission dynamics of COVID-19 While analyzing different regions of Italy it was found that Lombardia was the hardest hit and had the highest number of infectives. We have also forecasted the future scenario of the pandemic in Italy. The model predicts that the COVID-19 epidemic shall die out from the worst affected Lombardia region by approximately by November 2020. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.