Wavelet Collocation Method for HIV-1/HTLV-I Co-Infection Model Using Hermite Polynomial.

In this study, the dynamic behavior of fractional order co-infection model with human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type I (HTLV-I) is analyzed using operational matrix of Hermite wavelet collocation method. Also, the uniqueness and existence of solutions are calculated based on the fixed point hypothesis. For the fractional order co-infection model, its positivity and boundedness are demonstrated. Furthermore, different types of Ulam-Hyres stability are also discussed. The numerical solution of the model are obtained by using the operational matrix of the Hermite wavelet approach. This scheme is used to solve the system of nonlinear equations that are very fruitful and easy to implement. Additionally, the stability analysis of the numerical scheme is explained. The mathematical model taken in this work incorporates the biological characteristics of both HIV-1 and HTLV-I. After that all the equilibrium points of the fractional order co-infection model are found and their existence conditions are explored with the help of the Caputo derivative. The global stability of all equilibrium points of this model are determined with the help of Lyapunov functions and the LaSalle invariance principle. Convergence analysis is also discussed. Hermite wavelet operational matrix methods are more accurate and convergent than other numerical methods. Lastly, variations in model dynamics are found when examining different fractional order values. These findings will be valuable to biologists in the treatment of HIV-1/HTLV-I.