Numerical dynamics and optimal control for multi-strain age-structured epidemic model

In this paper, a novel age-structured epidemiological model that simultaneously considers multiple viral strains is proposed. We develop a numerical framework for the study of the dynamics and optimal control by a linearly implicit Euler method, in which the biological meaning is unconditionally preserved. The first order convergence of numerical solutions in a finite time is derived from a uniform numerical boundedness. Moreover, the numerical dynamics are determined by a numerical basic reproduction number $R_h$ , which reflects the asymptotic stability of the equilibrium points. The abstract framework offers an effective and unified approach to study the long-time behaviour of multi-strain epidemic models that cover a wide variety of well-known models, which also provides a numerical optimal control strategy of the multi-strain age-structured SIR model. Finally, some numerical simulations illustrate the verification and the efficiency of our results.