article · Scientific Reports
A fractional-order mathematical model was developed to analyse the transmission dynamics and control of monkeypox infection in humans, accounting for imperfect vaccination. The formulation initially used integer-order differential equations before being extended to a fractional-order derivative with a power law to capture disease dynamics more deeply. Model parameters were calibrated using cumulative reported cases from the United States between May and October 2022 alongside published demographic data. Mathematical analysis established sufficient conditions for the existence and uniqueness of solutions, and demonstrated the global stability of the model equilibria using the Lyapunov function method. Numerical simulations conducted via the fractional Adams-Bashforth-Moulton technique demonstrated how different fractional orders and epidemiological parameters influence the trajectory and control of the disease.
Understanding how imperfect vaccination affects monkeypox outbreaks helps epidemiologists evaluate transmission patterns. By using fractional-order derivatives, this approach captures complex disease dynamics that standard models may miss, offering deeper theoretical insights into how intervention parameters alter the course of viral spread during an epidemic.
This work represents early-stage theoretical and numerical research. It could potentially assist public health agencies and disease surveillance software developers seeking improved mathematical frameworks to model vaccination effects. However, the abstract does not describe any software implementation or decision-support tool, indicating the research is distant from real-world application.
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This present paper aims to examine various epidemiological aspects of the monkeypox viral infection using a fractional-order mathematical model. Initially, the model is formulated using integer-order nonlinear differential equations. The imperfect vaccination is considered for human population in the model formulation. The proposed model is then reformulated using a fractional order derivative with power law to gain a deeper understanding of disease dynamics. The values of the model parameters are determined from the cumulative reported monkeypox cases in the United States during the period from May 10th to October 10th, 2022. Besides this, some of the demographic parameters are evaluated from the population of the literature. We establish sufficient conditions to ensure the existence and uniqueness of the model's solution in the fractional case. Furthermore, the stability of the endemic equilibrium of the fractional monkeypox model is presented. The Lyapunov function approach is used to demonstrate the global stability of the model equilibria. Moreover, the fractional order model is numerically solved using an efficient numerical technique known as the fractional Adams-Bashforth-Moulton method. The numerical simulations are conducted using estimated parameters, considering various values of the fractional order of the Caputo derivative. The finding of this study reveals the impact of various model parameters and fractional order values on the dynamics and control of monkeypox.
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DOI: 10.1038/s41598-023-40745-x
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