Many studies have shown that faced with an epidemic, the effect of fear on human behavior can reduce the number of new cases. In this work, we consider an SIS-B compartmental model with fear and treatment effects considering that the disease is transmitted from an infected person to a susceptible person. After model formulation and proving some basic results as positiveness and boundedness, we compute the basic reproduction number $ \mathcal R_0 $ and compute the equilibrium points of the model. We prove the local stability of the disease-free equilibrium when $ \mathcal R_0 < 1 $. We study then the condition of occurrence of the backward bifurcation phenomenon when $ \mathcal R_0\leq1 $. After that, we prove that, if the saturation parameter which measures the effect of the delay in treatment for the infected individuals is equal to zero, then the backward bifurcation disappears and the disease-free equilibrium is globally asymptotically stable. We then prove, using the geometric approach, that the unique endemic equilibrium is globally asymptotically stable whenever the $ \mathcal R_0 > 1 $. We finally perform several numerical simulations to validate our analytical results.

The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient ($f^{{}^{\prime }}\left(\eta \right)$) enhances with the higher values of the Hall and shrinking parameters ($m,\varrho$), while it reduces with magnetic parameter and Weissenberg number ($M,We$). The y-component of fluid velocity ($g\left(\eta \right)$) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature $\theta \left(\eta \right)$ enhances with the increasing values of radiation parameter ($Rd$) and Dufour number ($Du$), while it drops with the rising Prandtl number ($Pr$). The concentration field ($\varphi \left(\eta \right)$) augments with the rising Soret number ($Sr$) while drops with the augmenting Schmidt number ($Sc$). The variation of the skin friction coefficients ($C_{fx}$ and $C_{fz}$), Nusselt number ($N{u}_x$) and Sherwood number ($S{h}_x$) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

We investigate a general sequential hybrid class of fractional differential equations in the Caputo and Atangana–Baleanu fractional senses of derivatives. We consider the existence and uniqueness of solutions and the Hyers–Ulam (H-U) stability for a general class. We use the Banach and Leray–Schauder alternative theorems for the existence criteria. With the help of nonnegative Green’s functions, the fractional-order class is turned into m-equivalent integral forms. As an application of our problem, a fractional-order smoking model in terms of the Atangana–Baleanu derivative is presented as a particular case.

Hypertension (HTN) is a globally prevalent non-communicable disease contributing significantly to cardiovascular (CV) morbidity and mortality. In achieving control of HTN, therapeutic adherence plays a crucial role. Studies from India identify varying rates of adherence to antihypertensive medications. Multiple factors determine treatment adherence in HTN. In India, factors such as lower socioeconomic status, health literacy, asymptomatic nature of disease, forgetfulness, cost of medications, and duration of HTN determine the adherence. An excellent physician-patient relationship incorporating adequate counseling along with the use of other methods can identify poor adherence. Improving adherence necessitates incorporating a multipronged approach with strategies directed at physicians, patients, and health systems. With innovation in therapeutics, the pharmaceutical sector can contribute significantly to improve adherence. Furthermore, increasing adherence to lifestyle interventions can help achieve better HTN control and improve CV outcomes. In the Indian context, more emphasis is necessary on patient education, enhanced physician-patient relationship and communication, increased access to health care, and affordability in improving therapeutic adherence in HTN.