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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

COVID-19 has dramatically changed people's mobility geste patterns and affected the operations of different functional spots. In the environment of the successful reopening of countries around the world since 2022, it's pivotal to understand whether the reopening of different types of locales poses a threat of wide epidemic transmission. In this paper, by establishing an epidemiological model based on mobile network data, combining the data handed by the Safegraph website, and taking into account the crowd inflow characteristics and the changes of susceptible and latent populations, the trends of the number of crowd visits and the number of epidemic infections at different functional points of interest after the perpetration of continuing strategies were simulated. The model was also validated with daily new cases in ten metropolitan areas in the United States from March to May 2020, and the results showed that the model fitted the evolutionary trend of realistic data more accurately. Further, the points of interest were classified into risk levels, and the corresponding reopening minimum standard prevention and control measures were proposed to be implemented according to different risk levels. The results showed that restaurants and gyms became high-risk points of interest after the perpetration of the continuing strategy, especially the general dine-in restaurants were at higher risk levels. Religious exertion centers were the points of interest with the loftiest average infection rates after the perpetration of the continuing strategy. Points of interest such as convenience stores, large shopping malls, and pharmacies were at a lower risk for outbreak impact after the continuing strategy was enforced. Based on this, continuing forestallment and control strategies for different functional points of interest are proposed to provide decision support for the development of precise forestallment and control measures for different spots. [ABSTRACT FROM AUTHOR]