The existence of man is dependant on nature. The peaceful existence is distributed either by man-made devastations or by natural damages. This study focuses on the contagious model of fractional order pine wilt disease employing the q-HATM (q-homotopy analysis transform method) to the leading fractional operator Atangana-Baleanu (AB) to arrive at better comprehension. The outgrowth are exhibited in the forms of figures and tables. At last the paper helps to analyse the practical theory and assists to predict its manner that correspond the guidelines contemplate the replica.

The aim of this paper is to apply the Differential Transformation Method (DTM) to analyze and obtain the solution for the mathematical model described by the system of non-linear ordinary differential equations which describe the epidemiology of the most threatening virus called \textbf{Corona-virus} later labeled as COVID-19. Finally, the present study may help you to examine the wild class of real-world models and also aid to predict their behavior with respect to parameters considered in the model. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks, and potential control strategies using the mathematical model.