Dynamic strategies for mathematical models involving infectious and noninfectious diseases

Аннотация: Part 1: Mathematical model for Cancer dynamic system We consider a time-fractional cancer invasion system with nonlocal diffusion operator. We show the existence and uniqueness of weak solutions by adapting the Faedo-Galerkin method and some a priori estimates. In addition, finite element numerical scheme is implemented for the considered system. Further, various numerical computations are performed along the convergence analysis of the scheme. Keywords: cancer invasion dynamic system; fractional differential equations; reaction-diffusion system; weak solution; numerical solution.
Part 2: Mathematical model for Covid-19 dynamic system We use discrete analysis and variable order calculus to establish a class of SEIQR model incorporating COVID-19 epidemic. We start to investigate the well-possedness of solution. Then, we show the disease-free and the endemic equilibrium points appropriately. Moreover, the local asymptotic stability of the model is analyzed. Further, we develop a discrete variable-order optimal control problem directed to COVID-19 properties, utilizing a discrete mathematical model featuring a variable-order difference. At end, we present some numerical simulations to support our finding.