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At this moment in time, an outbreak of COVID-19 is transmitting from human to human. Different parts have different quality of life (e.g., India compared to Russia), which implies the impact varies in each part of the world. Although clinical vaccines are available to cure, the question is how to minimize the spread without considering the vaccine. In this paper, via a mathematical model, the transmission dynamics of novel coronavirus with quarantine and isolation facilities have been proposed. The examination of the proposed model is set in motion with the boundedness and positivity of the solution, sole disease-free equilibrium, and local stability. Then, the condition for the existence of sole endemic equilibrium and its local stability has established. In addition, the global stability of the endemic equilibrium for a special case has been investigated. Further, it has shown that the system undergoes a transcritical bifurcation. A threshold analysis has also performed to examine the effect of quarantine on transmission dynamics. Lastly, numerical simulations are giving support to theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to answering some questions using a mathematical model by analyzing India's first and second phases of the COVID-19 pandemic. A new mathematical model is introduced with a nonmonotonic incidence rate to incorporate the psychological effect of COVID-19 in society. The paper also discusses the local stability and global stability of an endemic equilibrium and a disease-free equilibrium. The basic reproduction number is evaluated using the proposed COVID-19 model for disease spread in India based on the actual data sets. The study of nonperiodic solutions at a positive equilibrium point is also analyzed. The model is rigorously studied using MATLAB to alert the decision-making bodies to hinder the emergence of any other pandemic outbreaks or the arrival of subsequent pandemic waves. This paper shows the excellent prediction of the first wave and very commanding for the second wave. The exciting results of the paper are as follows: (i) psychological effect on the human population has an impact on propagation; (ii) lockdown is a suitable technique mathematically to control the COVID spread; (iii) different variants produce different waves; (iv) the peak value always crosses its past value. [ABSTRACT FROM AUTHOR]

In this paper, we have proposed an SVEIQR compartmental model modifying the classical SEIR model with inclusion of vaccinated and quarantined classes to explain the COVID-19 outbreak mathematically. We have calibrated our model with the daily COVID-19 data reported by the WHO coronavirus dashboard. To observe the disease dynamics of COVID-19, a detailed stability analysis of the proposed SVEIQR model is carried out. Our results show that the disease free equilibrium (DFE) is stable if the basic reproduction number is less than unity and unstable otherwise. Moreover, endemic equilibrium (EE) is found to be stable when certain restrictions hold. The expression for effective reproduction number has been derived analytically and its value is calculated based on the reported cases. Sensitivity analysis of effective reproduction number is performed employing PRCCs and Latin hypercube scheme. We have compared short-term and long-term transmission dynamics of COVID-19 for India with different levels of vaccination and without control strategies. The impact of different degrees of control interventions is ascertained with the numerical simulation of the model. [ABSTRACT FROM AUTHOR]

The analysis of problematic mathematical texts, particularly from India, has required the introduction of a new category of rigorous discourse, apodictic discourse. In this second part, we show that its introduction clarifies the approach to epistemic cultures. We also show that the notion of fantasy echo is relevant in Epistemology, as suggested by J.W. Scott. We then continue our earlier analysis of Brahmagupta's Prop. 12.21-32 on the cyclic quadrilateral and identify discursive strategies that enable him to convey definitions, hypotheses and derivations encoded in the very structure of the propositions stating his new results. We also show that the statements of mathematical formulae in words also follow definite discursive patterns. [ABSTRACT FROM AUTHOR]