A fractional-order two-strain SVIR model with stability analysis

The outbreak and spread of infectious diseases has become a worldwide concern, and during the spread of infectious diseases, viruses have been found to evolve and diverge into different strains. Based on this phenomenon, the mathematical and biological properties of a multi-strain infectious disease model with vaccination have been studied. In this paper, a fractional-order two-strain SVIR model is proposed. Specifically, the model incorporates vaccine protection that follows a power-law tail distribution and where the vaccine affects the two-strain differently. And the fractional-order derivative form is given by derivation because its memory properties can better characterize the effect of vaccine protection. Meanwhile, we derive an explicit expression for the basic reproduction number of the two-strain and clarify its crucial role in governing the dynamics of the system. The stability results for the fractional-order model are given with the help of Routh-Hurwitz and Lyapunov methods. Moreover, it has been found that the spread of the two-strain of the infectious disease has different effects under different thresholds. Finally, the spread of COVID-19 in India is considered as a real case study to verify the rationality of the proposed model.