article · Scientific Reports
A fractional-order mathematical model simulates the transmission dynamics of COVID-19 while incorporating containment measures such as face masks and social distancing. The framework divides the population into susceptible, infected, treated, and recovered compartments, with susceptible individuals split into two distinct subcategories. Mathematical evaluations confirm the positivity and boundedness of the solutions, alongside establishing equilibrium points and stability conditions. Solutions are derived using the Laplace Adomian decomposition method and compared against numerical simulations. The analytical framework is validated using real-world epidemiological data from Italy, demonstrating strong alignment with observed trends. Parameter analyses show that strict containment measures and reduced contact rates allow the system to achieve epidemiological stabilisation much faster. Conversely, the absence of confinement protocols prolongs the timeline to stabilisation and results in a higher overall burden of infection across the population.
Understanding how non-pharmaceutical interventions influence disease spread helps public health authorities plan containment strategies. By combining fractional calculus with analytical and numerical solving methods, this framework offers an accurate means to forecast infection trajectories. Demonstrating the direct link between strict confinement rules and faster epidemic stabilisation provides evidence to guide resource allocation and social distancing mandates during viral outbreaks.
The model provides an analytical foundation for epidemic forecasting tools that could be used by public health planners, epidemiologists, and municipal decision-makers assessing intervention policies. Because the work is validated against historical Italian infection data using mathematical and numerical simulations, it remains at the stage of applied mathematical research. Moving towards operational use would require integration into accessible software packages and testing across diverse, real-time epidemiological settings.
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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.
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DOI: 10.1038/s41598-023-50889-5
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