ABSTRACT
Coronavirus disease 2019 (COVID-19), an infection that is highly contagious. It has a regrettable effect on the world and has resulted in more than 4.6 million deaths to date (July 2021). For this contagious disease, numerous nations implemented control measures. Every country has vaccination programs in place to achieve the best results. This research is done in two stages, including partial and complete vaccination, to enhance the efficiency and effectiveness of the vaccination. Our study found that receiving this vaccination lowers the risk of contracting a disease and its side effects, such as severity, hospitalization, need for oxygen, admission to the intensive care unit, and infection-related death. Taking into account, the system is built using fractional-order Caputo sense nonlinear differential equations. A basic reproduction number is calculated to determine the transmission rate. The bifurcation analysis predicts chaotic behavior of a system for this threshold value. The suggested system's recovery rate is optimized using fractional optimum controls. For the fractional-order differential equation, numerical results are simulated using MATLAB software using real-validated data (July 2021).
ABSTRACT
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.
ABSTRACT
At the end of 2019, the novel coronavirus (COVID-19) outbreak was identified in Wuhan city of China. Because of its profoundly infectious nature, it was converted into a pandemic in a very short period. Globally, 6,291,764 COVID-19 confirmed cases, and a total of 374,359 deaths are reported as of 1st June 2020;nevertheless, the circumstances become more and more critical over time. Controlling this global pandemic has necessitated extensive strategies putting into practice. Based on the intensity of the epidemic, the model discriminates area into three different types of zones, and this distinction is crucial to construct various effective strategies for all three types of zones separately. The threshold value of the COVID-19 based on the data from zone-wise distribution of Indian districts from 15th April to 3rd May 2020 is calculated. Furthermore, the model is modified in a multi-group model to analyse the global transmission of COVID-19. Optimal control theory is applied to the model. Five control strategies are included based on the level of intensity of COVID-19.
ABSTRACT
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. As on 29 March 2020, the novel corona virus 2019 (COVID-19) has affected 199 countries and territories, causing 683,536 positive cases and 32,139 deaths. 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 the 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, the effect of control strategies on the model is analysed graphically by simulatin'g the model numerically. [ABSTRACT FROM AUTHOR] Copyright of International Journal of Mathematics & Mathematical Sciences is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)