A fractional-order two-strain epidemic model with two vaccinations

In this research paper, we extended an existing SIR epidemic integer model containing two strains and two vaccinations by using a system of fractional ordinary differential equations in the sense of Caputo derivative of order σ ∈ (0, 1]. Four equilibrium points were established which are disease free equilibrium, strain1 disease free equilibrium, strain2 disease free equilibrium and endemic equilibrium. Explicit analysis of the equilibrium points of the model was given by applying fractional calculus and Routh-Hurwitz criterion. Stability analysis of the equilibrium points was carried out by employing the Jacobian matrix. Numerical simulations were iterated to support the analytic results. It was shown that when both of the reproduction numbers R1 and R2 are less than one, the disease die out over time and while it persist in relation to the thriving strain when either of them is greater than one. We also studied the effect of vaccine. With the fractional order technique, the memory effect of the system is made visible and hence easier to predict.