Dynamics of a fractional epidemiological model with disease infection in both the populations.

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings.

Novel Dynamic Structures of 2019-nCoV with Nonlocal Operator via Powerful Computational Technique.

In this study, we investigate the infection system of the novel coronavirus (2019-nCoV) with a nonlocal operator defined in the Caputo sense. With the help of the fractional natural decomposition method (FNDM), which is based on the Adomian decomposition and natural transform methods, numerical results were obtained to better understand the dynamical structures of the physical behavior of 2019-nCoV. Such behaviors observe the general properties of the mathematical model of 2019-nCoV. This mathematical model is composed of data reported from the city of Wuhan, China.

A new study of unreported cases of 2019-nCOV epidemic outbreaks.

2019-nCOV epidemic is one of the greatest threat that the mortality faced since the World War-2 and most decisive global health calamity of the century. In this manuscript, we study the epidemic prophecy for the novel coronavirus (2019-nCOV) epidemic in Wuhan, China by using q-homotopy analysis transform method (q-HATM). We considered the reported case data to parameterise the model and to identify the number of unreported cases. A new analysis with the proposed epidemic 2019-nCOV model for unreported cases is effectuated. For the considered system exemplifying the model of coronavirus, the series solution is established within the frame of the Caputo derivative. The developed results are explained using figures which show the behaviour of the projected model. The results show that the used scheme is highly emphatic and easy to implementation for the system of nonlinear equations. Further, the present study can confirm the applicability and effect of fractional operators to real-world problems.

New numerical surfaces to the mathematical model of cancer chemotherapy effect in Caputo fractional derivatives.

In this paper, we apply the q-homotopy analysis transform method to the mathematical model of the cancer chemotherapy effect in the sense of Caputo fractional. We find some new approximate numerical results for different values of parameters of alpha. Then, we present novel simulations for all cases of results conducted by considering the values of parameters of alpha in terms of two- and three-dimensional figures along with tables including critical numerical values.