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Streszczenie:
In the work, author’s presents a very significant and important issues related to the health of mankind’s. Which is extremely important to realize the complex dynamic of inflected disease. With the help of Caputo fractional derivative, We capture the epidemiological system for the transmission of Novel Coronavirus-19 Infectious Disease (nCOVID-19). We constructed the model in four compartments susceptible, exposed, infected and recovered. We obtained the conditions for existence and Ulam’s type stability for proposed system by using the tools of non-linear analysis. The author’s thoroughly discussed the local and global asymptotical stabilities of underling model upon the disease free, endemic equilibrium and reproductive number. We used the techniques of Laplace Adomian decomposition method for the approximate solution of consider system. Furthermore, author’s interpret the dynamics of proposed system graphically via Mathematica, from which we observed that disease can be either controlled to a large extent or eliminate, if transmission rate is reduced and increase the rate of treatment.

Słowa kluczowe:
Fractional Derivatives, Fixed point theory, Ulams type Stabilities, Mathematical modeling, Approximate Solutions, Laplace-Adomian decomposition method