Throughout the globe, mankind is in vastly infected situations due to a cruel and destructive virus called coronavirus (COVID-19). The pivotal aim of the present investigation is to analyze and examine the evolution of COVID-19 in India with the available data in two cases first from the beginning to 31st March and beginning to 23rd April in order to show its exponential growth in the crucial period. The present situation in India with respect to confirmed, active, recovered and deaths cases have been illustrated with the aid of available data. The species of novel virus and its stages of growth with respect some essential points are presented. The exponential growth of projected virus by the day-to-day base is captured in 2D plots to predict its developments and identify the needs to control its spread on mankind. Moreover, the SEIR model is considered to present some interesting consequences about COVID-19 within the frame of fractional calculus. A newly proposed technique called q-Homotopy analysis transform method (q-HATM) is hired to find the solution for the nonlinear system portraying projected model and also presented the existence and uniqueness of the obtained results with help of fixed point theory. The behaviour has been captured with respect to fractional order and time.
In this research paper, the HIV-1 infection of CD4+ T-cells fractional mathematical model with the effect of antiviral drug therapy is handled by applying three new computational schemes to this biological model to investigate its analytical explicit wave solutions. This mathematical model is used to predict the evolution of the population dynamical systems involving virus particles. The modified Khater method, the extended simplest equation method, and sech–tanh method with a new fractional operator (Atangana–Baleanu derivative operator) is employing to find the analytical solutions in various distinct new formulas of the biological suggested model. Moreover, the stability of the obtained solutions is investigated by using the characterizes of the Hamiltonian system to show their applicability in making the antivirals that protect our human life. Some plots are explained under specific conditions of the contained constants to reveal the dynamical behavior of the evolution of the population dynamical systems involving virus particles. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the used methods shows power, practical, and ability to apply to other nonlinear partial differential equations.