Ferrofluid is a one-of-a-kind substance that functions both as a magnetic solid and as a liquid. In this article, waterbased Fe3O4 and Mn-ZnFe2O4 nanofluids between parallel stretchable spinning discs are considered. To carry out the study, the influence of rotational viscosity in the flow, which is due to the difference in rotation between the fluid and magnetic particles, and the applied magnetic field are examined. Additional impacts incorporated to the novelty of the model are the variable viscosity and variable thermal conductivity. The Legendre-based collocation method (LBCM) is used to solve the set of governing equations. To ensure the code validity, a comparison with analytical results is conducted and an excellent consensus is accomplished. Comparisons of the pertinent parameters on the flow profiles are displayed in tabular and graphical forms. Analyses reveal that the ferromagnetic Fe3O4 nanofluid shows higher thermal conductivity strength than the ferromagnetic Mn-ZnFe2O4 nanoparticles. This study finds its usefulness in aerospace, biotechnology, medical sciences, material sciences, and so on.
Summary
A new mathematical model of tuberculosis (TB) featuring exogenous re‐infection and incomplete treatment is presented and analyzed. The model divides total population into susceptible, latently infected, actively infected (uninformed and enlightened), and treatment classes. The model with or without incomplete treatment exhibits backward bifurcation phenomenon, which is caused by the presence of exogenous re‐infection. However, further investigation reveals that the absence of incomplete treatment has the potential to reduce the backward bifurcation range significantly. The global dynamics of the TB model without exogenous re‐infection is completely determined by the basic reproduction number under certain modifications on parameters. Furthermore, the model is extended to include three time‐dependent control functions, such as public awareness campaign, treatment effort, and preventive control against incomplete treatment. The existence of the optimal control for the nonautonomous model is proven and the three controls are characterized using Pontryagin's maximum principle. Numerical simulations are performed to show the significance of singular implementation of each of the controls and combination of the three controls in minimizing the TB burden in the population.
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