Fractional commensurate model on COVID-19 with microbial co-infection: An optimal control analysis

Abstract

Crossover behaviors have always existed in the history of infectious pandemics due to a few distinct, erratic spread outlines. This research aims to investigate the crossover behavior of the proposed SVICR commensurate fractional model for the COVID-19 delta variant, considering microbial coinfections. A mathematical model in terms of Atangana-Baleanu Caputo (ABC) category fractional integrals takes into account the co-infection of mucormycosis in immunocompromised COVID-19 patients caused by microbial infections. ABC operators preserve the intact history of the happenings under contemplation through its nonsingular kernel. It is observed that the framed five-compartmental SVICR model is positively bounded on R5, the solution space. Two equilibrium points E0andEe$$ {E}_0\mathrm{and}\ {E}_e $$ representing the survival and annihilation of sickness respectively are contributed by the single population N(t), which is counted in five dependent compartments: S(t),V(t),I(t),C(t),andR(t).$$ \mathrm{S}\left(\mathrm{t}\right),\mathrm{V}\left(\mathrm{t}\right),\mathrm{I}\left(\mathrm{t}\right),\mathrm{C}\left(\mathrm{t}\right),\mathrm{and}\ \mathrm{R}\left(\mathrm{t}\right). $$ The bilinear growth rate of new additional infections from the contagious infectives over time 't' is viewed through the threshold metric R0.$$ {R}_0. $$ Lyapunov's stability function examines the parametric influences over the virulent spread globally. The significant focus is to investigate the Mucormycosis cases in COVID-19 patients with underlying diabetic complications. Diabetes mellitus is the major concern for several coinfections among COVID-19 recoveries. Aiming to minimalize the critical states, an Lagrangian-Hamiltonian optimum control structure is also performed for the SVICR model by introducing control variables in effect to tri-control probes of minimized contact rates, persuasive vaccinations, and glycemic control of post recovered diabetic patients. The hike in the Severity of the ailment due to fungal pathogens is studied through numerical convergence of predictor-corrector scheme and simulations. Using estimated parametric values from the statistical data of mucormycosis and infections of COVID-19 reported cases in India, the prominence of control effects are visualized graphically. To conclude, a complete qualitative analysis of the minimization problem is executed for different levels of control values. We avow that effective control intrusions would almost certainly decline the complexities associated with the viral pathogens. We have developed a novel epidemiological SVICR model involving microbial co-infections with ABC-type fractional equations for the double mutant COVID-19 ailment in INDIA. India has a heavy burden of mucormycosis cases among diabetic patients with hyperglycaemia from May 2021 to Sep 2021. One of the imperative features of this novel model is considering the transference among unvaccinated and vaccinated susceptible populations who are responsible for contagious spread around their area. The biological feasibility of the model is analyzed through boundedness and feasible invariant region.image