The asymptotic analysis of novel coronavirus disease via fractional-order epidemiological model

Abstract

We develop a model and investigate the temporal dynamics of the transmission of the novel coronavirus. The main sources of the coronavirus disease were bats and unknown hosts, which left the infection in the seafood market and became the major cause of the spread among the population. Evidence shows that the infection spiked due to the interaction between humans. Hence, the formulation of the model proposed in this study is based on human-to-human and reservoir-to-human interaction. We formulate the model by keeping in view the esthetic of the novel disease. We then fractionalize it with the application of fractional calculus. Particularly, we will use the Caputo–Fabrizio operator for fractionalization. We analyze the existence and uniqueness of the well-known fixed point theory. Moreover, it will be proven that the considered model is biologically and mathematically feasible. We also calculate the threshold quantity (reproductive number) to discuss steady states and to show that the particular epidemic model is stable asymptotically under some restrictions. We also discuss the sensitivity analysis of the threshold quantity to find the relative impact of every epidemic parameter on the transmission of the coronavirus disease. Both the global and local properties of the proposed model will be analyzed for the developed model using the mean value theorem, Barbalat’s lemma, and linearization. We also performed some numerical simulations to verify the theoretical work via some graphical representations.