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Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as a pandemic disease. Regrettably, the spread of the virus and mortality due to COVID-19 have continued to increase daily. The study is performed using the Atangana–Baleanu–Caputo operator with a harmonic mean type incidence rate. The existence and uniqueness of the solutions of the fractional COVID-19 epidemic model have been developed using the fixed point theory approach. Along with stability analysis, all the basic properties of the given model are studied. To highlight the most sensitive parameter corresponding to the basic reproductive number, sensitivity analysis is taken into account. Simulations are conducted using the first-order convergent numerical approach to determine how parameter changes influence the system’s dynamic behavior.

This work presents a theoretical numerical study of the bioconvection flow of Prandtl–Eyring nanofluid through a stretching cylinder with gyrotactic microorganisms. The mathematical model developed also incorporated the inclined magnetic field and heat generation effects. Further, stratification conditions are considered at the boundary of the stretched cylinder. The described flow problem conducting coupled high‐order partial differential equations (PDEs) is first reduced to the nonlinear system of ordinary differential equations (ODEs) by introducing suitable mathematical transformations. The resulting highly nonlinear flow equations are treated numerically by applying the shooting method. A comparison of the adapted method with previously reported data is also made to validate the presented results. The comparisons are in excellent agreement. The individual effect of controlling flow parameters/numbers on the flow profiles and physical quantities of engineering interest are represented graphically with physical descriptions. The significant results of the present analysis revealed that a rise in bioconvection Rayleigh number, thermal Grashof number, and angle of inclination boosts the velocity profile. The study shows that thermal stratification, mass stratification, and motile density stratification parameters diminish the temperature, concentration, and microorganism profiles, respectively. The nondimensional Sherwood number is decelerated significantly by thermophoresis and mass stratification parameters. [ABSTRACT FROM AUTHOR]

This paper addresses the dynamics of COVID‐19 using the approach of age‐structured modeling. A particular case of the model is presented by taking into account age‐free parameters. The sub‐model consisting of ordinary differential equations (ODEs) is investigated for possible equilibria, and qualitative aspects of the model are rigorously presented. In order to control the spread of the disease, we considered two age‐ and time‐dependent non‐pharmaceutical control measures in the age‐structured model, and an optimal control problem using a general maximum principle of Pontryagin type is achieved. Finally, sample simulations are plotted which support our theoretical work. [ABSTRACT FROM AUTHOR]