Volume 43_1_(2022)_37-59

On the asymptotic behavior and approximate solution of a varicella zoster model using the modified differential transform method
Oluwatayo M. Ogunmiloro, Michael O. Oke, Precious O. Ojakovo

Abstract. This article proposes a mathematical model describing the evolution and transmission of Varicella Zoster Virus (VZV) disease among classes of human individuals. The model is formulated to accommodate parameters and variables describing direct and indirect forms of transmission, re-activation of infectious shingles as well as the treatment and vaccination of susceptible births and immigrants. The model is analyzed and found to be positive, bounded and well posed. The controlled basic reproduction number Rvzv, obtained using the next generation matrix operator reveals that vaccination is effective as a control in creating a level herd immunity. Linearizing the model around the VZV - free equilibrium shows that the model is locally and globally asymptotically stable when Rvzv is less than unity. The approximate solution of the model system equations is obtained using the modified differential transform which involves the Differential Tranform Method (DTM) and the Laplace - Pade posttreatment technique (LP). The hybrid LPDTM technique is employed to enlarge the domain of convergence of the approximate solutions of the model. The model solutions using LPDTM is compared with the Fehlberg fourth order Runge - Kutta (RK45) via the Maple computational software to show the efficiency and convergence of the two methods through simulations. Further simulations carried out on the model reveal that timely vaccination and treatment are effective strategies in curtailing the spread of VZV infection in human and environmental host population

Rend. Mat. Appl. (7) 43 (2022) 37-59;  pdf