Stability Analysis and Optimal Control on a Multi-Strain Coinfection Model with Amplification and Vaccination

In this paper, a multi-strain coinfection model with amplification (or mutation) is established to characterize the interaction between common strain and amplified strain, as well as vaccination. The basic reproduction number R0 is derived, from which the criteria on the existence and local (or global) stability of equilibria (including disease-free, dominant-strain and coexistence-strain) are established. By analyzing the effectiveness of vaccination, we find that a critical inoculation level could make the disease eliminate when R0<1, while inefficient vaccines could cause backward bifurcation when R0<1. Based on sensitivity analysis and realistic control policy, the optimal strategy of disease control is obtained. The theoretical results are illustrated by numerical simulation and clinical data of COVID-19 in Morocco.