Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study

Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model's dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if (Formula presented.) is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter (Formula presented.) that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when (Formula presented.) for the imperfect vaccine case;the model is both stable globally asymptotically at the disease-free ((Formula presented.)) and endemic cases ((Formula presented.)). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number (Formula presented.). We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail. © 2023 by the authors.

Near-Real-Time Carbon Emission Accounting Technology Toward Carbon Neutrality

Climate change is the greatest environmental threat to humans and the planet in the 21st century. Global anthropogenic greenhouse gas emissions are one of the main causes of the increasing number of extreme climate events. Cumulative carbon dioxide (CO2) emissions showed a linear relationship with cumulative temperature rise since the pre-industrial stage, and this accounts for approximately 80% of the total anthropogenic greenhouse gases. Therefore, accurate and reliable carbon emission data are the foundation and scientific basis for most emission reduction policymaking and target setting. Currently, China has made clear the ambitious goal of achieving the peak of carbon emissions by 2030 and achieving carbon neutrality by 2060. The development of a finer-grained spatiotemporal carbon emission database is urgently needed to achieve more accurate carbon emission monitoring for continuous implementation and the iterative improvement of emission reduction policies. Near-real-time carbon emission monitoring is not only a major national demand but also a scientific question at the frontier of this discipline. This article reviews existing annual-based carbon accounting methods, with a focus on the newly developed real-time carbon emission technology and its current application trends. We also present a framework for the latest near-real-time carbon emission accounting technology that can be widely used. The development of relevant data and methods will provide strong database support to the policymaking for China's "carbon neutrality" strategy. Finally, this article provides an outlook on the future of real-time carbon emission monitoring technology.(c) 2022 THE AUTHORS. Published by Elsevier LTD on behalf of Chinese Academy of Engineering and Higher Education Press Limited Company. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Global patterns of daily CO2 emissions reductions in the first year of COVID-19

Observed daily changes in CO2 emissions from across the globe reveal the sectors and countries where pandemic-related emissions declines were most pronounced in 2020. Day-to-day changes in CO2 emissions from human activities, in particular fossil-fuel combustion and cement production, reflect a complex balance of influences from seasonality, working days, weather and, most recently, the COVID-19 pandemic. Here, we provide a daily CO2 emissions dataset for the whole year of 2020, calculated from inventory and near-real-time activity data. We find a global reduction of 6.3% (2,232 MtCO(2)) in CO2 emissions compared with 2019. The drop in daily emissions during the first part of the year resulted from reduced global economic activity due to the pandemic lockdowns, including a large decrease in emissions from the transportation sector. However, daily CO2 emissions gradually recovered towards 2019 levels from late April with the partial reopening of economic activity. Subsequent waves of lockdowns in late 2020 continued to cause smaller CO2 reductions, primarily in western countries. The extraordinary fall in emissions during 2020 is similar in magnitude to the sustained annual emissions reductions necessary to limit global warming at 1.5 degrees C. This underscores the magnitude and speed at which the energy transition needs to advance.