Kermack-McKendrick epidemic model is considered as the basis from which many other compartmental models were developed. But the development of fractional calculus applied to mathematical epidemiology is still ongoing and relatively recent. We provide, in this article, some interesting and useful properties of the Kermack-McKendrick epidemic model with nonlinear incidence and fractional derivative order in the sense of Caputo. In the process, we used the generalized mean value theorem (Odibat and Shawagfeh in Appl. Math. Comput. 186:286-293, 2007) extended to fractional calculus to conclude some of the properties. A model of the Kermack-McKendrick with zero immunity is also investigated, where we study the existence of equilibrium points in terms of the nonlinear incidence function. We also establish the condition for the disease free equilibrium to be asymptotically stable and provide the expression of the basic reproduction number.

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In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under different chemical kinetics through a channel in the presence of a heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. The Adomian decomposition method together with Pade approximation technique are used to obtain the solutions of the governing nonlinear non-dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis, irreversibility distribution ratio, Bejan number and the conditions for thermal criticality for different chemical kinetics are also presented.

A mathematical model for the phenomenon of penetration of fluid into permeable walls is developed for second grade fluids. The model is based on mechanical principles which involve normal stresses at the boundary and contact forces at the fluid-boundary interface. Stability of the rest state is proved. The results are compared to that for the simplified case of a Navier-Stokes fluid.

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