Designing a novel fractional order mathematical model for COVID-19 incorporating lockdown measures.

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible [Formula: see text], infected [Formula: see text], treated [Formula: see text], and recovered [Formula: see text] with the susceptible category further divided into two subcategories [Formula: see text] and [Formula: see text]. In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner.

On nonlinear dynamics of a fractional order monkeypox virus model.

In this work, we examine a fractional-order model for simulating the spread of the monkeypox virus in the human host and rodent populations. The employment of the fractional form of the model gives a better insight into the dynamics and spread of the virus, which will help in providing some new control measures. The model is formulated into eight mutually exclusive compartments and the form of a nonlinear system of differential equations. The reproduction number for the present epidemic system is found. In addition, the equilibrium points of the model are investigated and the associated stability analysis is carried out. The influences of key parameters in the model and the ways to control the monkeypox epidemic have been thoroughly examined for the fractional model. To ensure that the model accurately simulates the nonlinear phenomenon, we adapt an efficient numerical technique to solve the presented model, and the acquired results reveal the dynamic behaviors of the model. It is observed that when memory influences are considered for the present model, through Caputo fractional-order derivatives, they affect the speed and time taken by solution trajectories towards steady-state equilibria.