Recently the World Health Organization has declared the outbreak of a severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) as a pandemic, and declared it as Public Health Emergency of International Concern. More than 683,536 positive cases and 32,139 deaths caused by novel corona virus 2019 (COVID-19) has affected 199 countries and territories. This pandemic can transform into an extremely destructive form if we still do not take it seriously. In the present study, we propose a generalized SEIR model of COVID-19 to study the behaviour of its transmission under different control strategies. In the model, all possible cases of human to human transmission are taken care and its reproduction number is formulated to analyse accurate transmission dynamics of the coronavirus outbreak. Optimal control theory is applied in the model to pretend the impact of various intervention strategies, including voluntary quarantine, isolation of infected individuals, improving an individual's immunity and hospitalisation. Also, effect of the control strategies on model is analysed graphically by simulating the model numerically.

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

On 11 March 2020, the World Health Organization declared the outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) a pandemic and a Public Health Emergency of International Concern. As of 29 March 2020, coronavirus disease 2019 (COVID-19) has affected 199 countries and territories, resulting in 683,536 positive cases and causing 32,139 deaths. The pandemic has the potential to become extremely destructive globally if not treated seriously. In this study, we propose a generalized SEIR model of COVID-19 to study the behaviour of its transmission under different control strategies. In the model, all possible cases of human-to-human transmission are considered and its reproduction number is formulated to analyse the accurate transmission dynamics of the coronavirus outbreak. Optimal control theory is applied to the model to demonstrate the impact of various intervention strategies, including voluntary quarantine, isolation of infected individuals, improving an individual's immunity, and hospitalization. In addition, the effect of control strategies on the model is analysed graphically by simulating the model numerically.

Background: The first case of COVID-19 was reported in Wuhan, China in December 2019. The disease has spread to 210 countries and has been labeled as a pandemic by WHO. Modelling, evaluating, and predicting the rate of disease transmission is crucial for epidemic prevention and control. Our aim is to assess the impact of interstate and foreign travel and public health interventions implemented by the United States government in response to the Covid-19 pandemic. Methods: A disjoint mutually exclusive compartmental model is developed to study the transmission dynamics of the novel coronavirus. A system of non-linear differential equations was formulated and the basic reproduction number R0 was computed. The stability of the model was evaluated at the equilibrium points. Optimal controls were applied in the form of travel restrictions and quarantine. Numerical simulations were conducted. Results: Analysis shows that the model is locally asymptomatically stable, at endemic and foreigners free equilibrium points. Without any mitigation measures, infectivity and subsequent hospitalization of the population increase while placing interstates individuals and foreigners under quarantine, decreases the chances of exposure and subsequent infection, leading to an increase in the recovery rate. Conclusion: Interstate and foreign travel restrictions, in addition to quarantine, help in effectively controlling the epidemic.

Farming is the basic economy of any country. Soil fertility and water are key resources for yielding. The fractional order compartmental model is prepared in Caputo sense to improve the density of yield through diagnosed and undiagnosed soil. To measure the growing intensity of yield, the basic reproduction number is formulated using the next generation matrix method for integer order non-linear dynamical system. Local stability analysis is described for both the equilibrium points; undiagnosed soil free and optimum equilibrium point. Global stability is exhaustively computed by generating a Lyapunov function. With reference to the basic reproduction number, bifurcation analysis has been defined which expresses the chaotic nature of soil fertility. Moreover, optimal control theory is applied in the present fractional model to optimize yield. And optimality conditions are calculated with the help of Pontryagin maximum principle. The numerical simulation for different fractional orders is performed concerning validated data to analyze the behavior with respect to the order.