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The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain restrictions. The mathematical model has been numerically simulated using the predictor-corrector method to highlight the role played by fractional order in controlling the disease spread. Numerical simulations signify the fact that a vital role has been played by fractional order model over integer order model in determining the transmission of COVID-19. It can be visualized that the increment rate in the infectives is lower by taking into consideration the memory effect due to a previous exposure to COVID-19. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which is based on Lyapunov stability theory. To verify synchronization is achieved between the systems, we performed the numerical simulation. [ABSTRACT FROM AUTHOR]

In the present paper, we have determined the equations of motion of the Moon in spherical coordinate system using the gravitational potential of Earth. Using perturbation, equations of motion are reduced to a second order differential equation. From the solution, two types of resonance are observed: (i) due to the frequencies-rate of change of Earth's equatorial ellipticity parameter and Earth's rotation rate, and (ii) due to the frequencies-angular velocity of the bary-center around the sun and Earth's rotation rate. Resonant curves are drawn where oscillatory amplitude becomes infinitely large at the resonant points. The effect of Earth's equatorial ellipticity parameter and resistive force on the resonant curve is analyzed. From the graphs it is observed that the effect of Earth's equatorial ellipticity on the resonant curve is very small while the effect of resistive force is significant. It is also observed that oscillatory amplitude decreases when the magnitude of resistive force increases. Finally, the phase portrait is analyzed when the system is free from forces. Orbits in the phase space are also studied by applying the method of Poincare section. A necessary condition for the bifurcation is derived at the end. [ABSTRACT FROM AUTHOR]

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe's problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere are analyzed. This small solid sphere is moving inside the first primary which is a homogeneous incompressible viscous fluid whose hydrostatic equilibrium figure is an oblate spheroid. The second primary is a finite straight segment. The existence of the equilibrium points is discussed after deriving the pertinent equations of motion of the small solid sphere. It is found that viscosity does not affect the location and number of equilibrium points but affects the stability as it converts the marginal stability to asymptotic stability. However, oblateness affects the locations of the equilibrium points. Applicability of the results of this study to an astrophysical problem is discussed, and we have calculated a lower bound on the ratio of the orbital radius and the total mass of the primaries of an astrophysical problem to which the results obtained may be applied. This ratio is called the scaling factor. [ABSTRACT FROM AUTHOR]

Coronavirus Disease 2019 (COVID-19) is spreading across the world, and vaccinations are running parallel. Coronavirus has mutated into a triple-mutated virus, rendering it deadlier than before. It spreads quickly from person to person by contact and nasal or pharyngeal droplets. The COVID-19 database 'Our World in Data' was analyzed from February 24, 2020, to September 26, 2021, and predictions on the COVID positives and their mortality rate were made. Factors such as Vaccine data for the First and Second Dose vaccinated individuals and COVID positives that influence the fluctuations in the COVID-19 death ratio were investigated and linear regression analysis was performed. Based on vaccination doses (partial or complete vaccinated), models are created to estimate the number of patients who die from COVID infection. The estimation of variance in the datasets was investigated using Karl Pearson's coefficient. For COVID-19 cases and vaccination doses, a quartic polynomial regression model was also created. This predictor model helps to predict the number of deaths due to COVID-19 and determine the susceptibility to COVID-19 infection based on the number of vaccine doses received. SVM was used to analyze the efficacy of models generated. [ABSTRACT FROM AUTHOR]

In the present article, the periodic solutions of the N‐body with quasi‐homogeneous potential in the Sitnikov sense by applying the multiple methods of scale (MMS) and Lindstedt–Poincaré (LP) technique are obtained. However, these methods are used to find the approximate periodic solutions in the closed form by eliminating the secular terms. In addition of the Newtonian potential and forces, we consider that the big bodies create quasi‐homogeneous potentials. We add the inverse cubic corrective term to the inverse square Newtonian law of gravitation, in order to approximate the various phenomena due to the shape of the bodies or the radiation emitting from them. We study the Sitnikov motion in the N‐bodies under this consideration. We, further, analyzed the obtain approximate periodic solutions of the Sitnikov motion, for ν=2,7 by using the MMS and LP‐method, in closed form. The numerical comparisons are presented in the first and second approximated solutions obtained by using MMS and numerical solutions obtained by LP‐method are illustrated graphically. The effect of initial conditions on the solutions of the Sitnikov motion is illustrated graphically obtained by both the techniques. It is observed that the choice of initial conditions plays a crucial role in the numerical and approximate solutions. [ABSTRACT FROM AUTHOR]

The restricted three‐body problem, where the primaries are magnetic dipoles, is discussed. In the predefined interval, the effect of the varying values of mass parameter μ and the angular velocity ω on the parametric variation of locations of the equilibrium points are illustrated. Indeed, the influence of the values of the ratio λ of the magnetic moments in the presence of angular velocity ω on the topology of the basins of convergence is discussed. The bivariate version of the well‐known Newton–Raphson scheme is used to illustrate the basins of convergence on the configuration (x, y) plane. In addition, the correlations betwixt the basins of convergence associated to the equilibrium points and the linked number of iterations required to assure the preassumed precision are discussed. In this study, a rigorous and structured numerical investigation are illustrated by exhibiting how the values of λ and ω have significant influence on the shape, the topology and also the degree of fractality of the domain of basins of convergence. The results and outcomes of present study strongly indicate that the parameters ω,μ, and λ have significant influence in the electromagnetic binary system. [ABSTRACT FROM AUTHOR]

• The axisymmetric restricted five-body problem within the frame of variable mass has been studied. • The positions of libration points are illustrated. • The basins of convergence are unveiled. • The basin entropy is presented. The present manuscript reveals the existence and stability of the libration points (LPs) in the axisymmetric restricted five-body problem (AR5BP) in which mass of the fifth particle varies with respect to time as per Jeans' law. It has been assumed that the four bodies P i with masses m i , i = 1 , 2 , ... , 4 (when m 3 = m 4 = m ˜) form an axisymmetric convex configuration. The system of differential equations which govern the motion of the test particle (whose mass is variable) moving under the gravitational influence of the four primaries, have been presented, indeed, these equations are different from those of the test particle with constant mass in the AR5BP. We have determined the in-plane and out-of-plane LPs along with their linear stability. Furthermore, it is observed that the existence of these LPs depends not only on the angle parameters α and β but also on the parameters occur due to variation in mass namely γ (0 < γ ≤ 1) and σ (0 ≤ σ ≤ 2.2 , a proportionality constant occurs in Jeans' law). Moreover, we have investigated the evolution of the regions of possible motion as function of variable mass parameters where the fifth body can move freely. The topology of the basins of convergence (BoC) linked with the LPs as function of σ is unveiled by deploying the bivariate version of Newton-Raphson (NR) iterative method, and, in order to measure the uncertainty of the basins, the basin entropy is also evaluated. The co-relations between the domains of basins of convergence (DoBoC) and the required number of iterations to achieve predefined accuracy, and also with the corresponding probability distributions are illustrated. [ABSTRACT FROM AUTHOR]