ON THE ASYMPTOTIC BEHAVIOR AND APPROXIMATE SOLUTIONS OF VARICELLA ZOSTER
VIRUS MODEL USING MODIFIED DIFFERENTIAL TRANSFORM METHOD
Abstract
This article proposes a mathematical model describing the evolution and
transmission of Varicella Zoster Virus (VZV) over large groups of
individuals. The model was formulated to accommodate parameters and
variables describing direct and indirect forms of transmission,
re-activation of infectious shingles as well as treatment and
vaccination of susceptible births and influx of immigrants. The model
was analysed to be positive, bounded and well posed. The controlled
basic reproduction number Rvzv, obtained using the next generation
matrix operator reveal 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
solutions of the model system equations was obtained using the modified
differential transform which involves the Differential Transform Method
(DTM) and Laplace - Pade post-treatment technique (LPDTM). This
technique was employed to enlarge the domain of convergence of the
approximate solutions of the model. LPDTM was compared with the Fehlberg
fourth order Runge - Kutta (RKF45) via the MAPLE computational software
to show the accuracy of the results through simulations. Further
simulations carried out on the model reveal that timely vaccination and
treatment are eeffective strategies in containing VZV infection spread
in human and environmental host population.