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.

Mice and rats are important mammalian models in biomedical research. In contrast to other biomedical fields, work on sexual differentiation of brain and behavior has traditionally utilized comparative animal models. As mice are gaining in popularity, it is essential to acknowledge the differences between these two rodents. Here we review neural and behavioral sexual dimorphisms in rats and mice, which highlight species differences and experimental gaps in the literature, that are needed for direct species comparisons. Moving forward, investigators must answer fundamental questions about their chosen organism, and attend to both species and strain differences as they select the optimal animal models for their research questions.

In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of the citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold has been estimated to be  ∼ 3.41 as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 daily confirmed cases. The tally of cumulative infected cases could reach  ∼ 20, 100 cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations enlightened the fact that if the fractional order α is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0  < α <  1) leads to the delaying of the epidemic peaks.

Sex differences in the nervous system come in many forms. Although a majority of sexually dimorphic characteristics in the brain have been described in older animals, mechanisms that determine sexually differentiated brain characteristics often operate during critical perinatal periods. Both genetic and hormonal factors likely contribute to physiological mechanisms in development to generate the ontogeny of sexual dimorphisms in brain. Relevant mechanisms may include neurogenesis, cell migration, cell differentiation, cell death, axon guidance and synaptogenesis. On a molecular level, there are several ways to categorise factors that drive brain development. These range from the actions of transcription factors in cell nuclei that regulate the expression of genes that control cell development and differentiation, to effector molecules that directly contribute to signalling from one cell to another. In addition, several peptides or proteins in these and other categories might be referred to as ‘biomarkers’ of sexual differentiation with undetermined functions in development or adulthood. Although a majority of sex differences are revealed as a direct consequence of hormone actions, some may only be revealed after genetic or environmental disruption. Sex differences in cell positions in the developing hypothalamus, and steroid hormone influences on cell movements in vitro, suggest that cell migration may be one target for early molecular actions that impact brain development and sexual differentiation.

Highlights The fractional-order COVID-19 model in new generalised Caputo sense is formulated to study the prediction of COVID-19 epidemic peaks in the world. The existence and uniqueness of solutions are proved by the applications of Fixed point theory. The predictor- corrector method has been used to construct the numerical simulations of the proposed fractional model. The stability analysis of the constructed numerical scheme is performed.