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Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

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This article aims at investigating stability properties for a class of discrete fractional equations with anti-periodic boundary conditions of fractional order δ ∈ (3, 4]. Utilizing contraction mapping principle and fixed point theorem due to Brouwer [2], new criteria for the uniqueness and existence of the solutions are developed and two types of Ulam stability are analyzed. The theoretical outcomes are corroborated with examples.

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