Stability analysis and optimal control on a multi-strain coinfection model with amplification and vaccination

Abstract

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.

Keywords

• Multi-strain
• Amplification
• Vaccination
• Backward bifurcation
• Optimum control