Mathematical assessment of monkeypox disease with the impact of vaccination using a fractional epidemiological modeling approach.

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.

The prevalence and management of chronic pain in the Chinese population: findings from the China Pain Health Index (2020).

BACKGROUND: Chronic pain is a common disease; about 20% of people worldwide suffer from it. While compared with the research on the prevalence and management of chronic pain in developed countries, there is a relative lack of research in this field in China. This research aims to construct the China Pain Health Index (CPHI) to evaluate the current status of the prevalence and management of chronic pain in the Chinese population. METHODS: The dimensions and indicators of CPHI were determined through literature review, Delphi method, and analytical hierarchy process model, and the original values ​​of relevant indicators were obtained by collecting multi-source data. National and sub-provincial scores of CPHI (2020) were calculated by co-directional transformation, standardization, percentage transformation of the aggregate, and weighted summation. RESULTS: The highest CPHI score in 2020 is Beijing, and the lowest is Tibet. The top five provinces are Beijing (67.64 points), Shanghai (67.04 points), Zhejiang (65.74 points), Shandong (61.16 points), and Tianjin (59.99 points). The last five provinces are Tibet (33.10 points), Ningxia (37.24 points), Guizhou (39.85 points), Xinjiang (39.92 points), and Hainan (40.38 points). The prevalence of chronic pain is severe in Heilongjiang, Chongqing, Guizhou, Sichuan, and Fujian. Guizhou, Hainan, Xinjiang, Beijing, and Guangdong display a high burden of chronic pain. The five provinces of Guangdong, Shanghai, Beijing, Jiangsu, and Zhejiang have better treatment for chronic pain, while Tibet, Qinghai, Jilin, Ningxia, and Xinjiang have a lower quality of treatment. Beijing, Shanghai, Qinghai, Guangxi, and Hunan have relatively good development of chronic pain disciplines, while Tibet, Sichuan, Inner Mongolia, Hebei, and Guizhou are relatively poor. CONCLUSION: The economically developed provinces in China have higher CPHI scores, while economically underdeveloped areas have lower scores. The current pain diagnosis and treatment situation in economically developed regions is relatively good, while that in financially underdeveloped areas is rather poor. According to the variations in the prevalence and management of chronic pain among populations in different provinces in China, it is necessary to implement chronic pain intervention measures adapted to local conditions.

The Effect of Carbon Emission Taxes on Environmental and Economic Systems.

Carbon dioxide is believed widely to be the major contributor to global warming. Policymakers worldwide are turning to tax policies in an effort to abate carbon emissions. China is the largest emitter of carbon emissions on our planet. The central government, as well as the local official, has introduced a series of environmental regulations, such as environmental protection tax and emissions trading system, to reduce carbon emissions and improve environmental quality. In the near future, the carbon emission tax is also expected to be implemented by the Chinese government. In order to analyze and predict the effect of the carbon emission tax on environmental and economic systems, we developed a four department dynamic stochastic general equilibrium model, which includes households, enterprises, the government, and the environment. The dynamic parameters were obtained using maximum likelihood estimation. In the comparative static-s analysis, we found that after the introduction of carbon emission tax, the level in environmental quality was substantially improved, whereas most economic variables were significantly reduced. Moreover, we used impulse responses functions to evaluate how one shock to the carbon emission tax affects the steady static values for these endogenous variables in our model. We found that the carbon emission tax shock has an instantaneous effect on the majority of economic variables, but it does not affect the environmental quality immediately. In addition, we tested the Porter hypothesis and found no evidence suggesting the statement regarding this hypothesis. Finally, we applied Bayesian estimation to assure our findings in this study, again.

Intrathecal Morphine Infusion Therapy via a Percutaneous Port for Refractory Cancer Pain in China: An Efficacy, Safety and Cost Utilization Analysis.

PURPOSE: Intrathecal morphine infusion therapy via a percutaneous port (IMITPP) has been used widely for its relatively low initial cost. However, there is scarce knowledge about IMITPP. In this study, we sought to evaluate efficacy, complications, and the interval required to achieve the cost equivalence of IMITPP in patients with refractory cancer pain in China. PATIENTS AND METHODS: A retrospective chart review was conducted on cancer patients who had received IMITPP at our hospital between April 2017 and April 2019. Data from the numeric pain rating scale and Karnofsky performance scores, and complications and costs related to IMITPP were collected from medical records. Daily analgesic costs before and after IMITPP were calculated based on the doses of opioids on admission and at discharge, respectively. The doses of systemic opioids before IMITPP were stratified into very high doses [VHD, oral morphine equivalent dose (OMED) >599 mg/day], high doses (HD, 300 mg/day ≤ OMED ≤ 599 mg/day), and regular doses (RD, OMED < 300 mg/day). RESULTS: Intrathecal morphine infusion therapy via a percutaneous port provided significant pain relief, but impaired activities of daily living in patients with refractory cancer pain. The commonly reported complications included nausea/vomiting and urinary retention, most of which were managed with symptomatic therapies. The median interval required to achieve cost equivalence was 11.44 months. The median intervals of VHD group and HD group were significantly shorter than that of RD group. CONCLUSION: Intrathecal morphine infusion therapy via a percutaneous port provided effective cancer pain management without causing serious complications. Patients with higher doses of systemic opioids would economically benefit from IMITPP in a shorter time.