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In this paper, we develop a new mathematical model for an in-depth understanding of COVID-19 (Omicron variant). The mathematical study of an omicron variant of the corona virus is discussed. In this new Omicron model, we used idea of dividing infected compartment further into more classes i.e asymptomatic, symptomatic and Omicron infected compartment. Model is asymptotically locally stable whenever R0<1 and when R0≤1 at disease free equilibrium the system is globally asymptotically stable. Local stability is investigated with Jacobian matrix and with Lyapunov function global stability is analyzed. Moreover basic reduction number is calculated through next generation matrix and numerical analysis will be used to verify the model with real data. We consider also the this model under fractional order derivative. We use Grunwald-Letnikov concept to establish a numerical scheme. We use nonstandard finite difference (NSFD) scheme to simulate the results. Graphical presentations are given corresponding to classical and fractional order derivative. According to our graphical results for the model with numerical parameters, the population's risk of infection can be reduced by adhering to the WHO's suggestions, which include keeping social distances, wearing facemasks, washing one's hands, avoiding crowds, etc.
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In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Similar models have been focused on by Julien Arino, Fred Brauer, Odo Diekmann, and their coauthors, but mostly in the case of "closed populations” (models with varying populations have been studied in the past only in particular cases, due to the difficulty of this endeavor). Our Arino–Brauer models contain SIR–PH models of Riano (2020), which are characterized by the phase-type distribution (Formula presented.), modeling transitions in "disease/infectious compartments”. The A matrix is simply the Metzler/sub-generator matrix intervening in the linear system obtained by making all new infectious terms 0. The simplest way to define the probability row vector (Formula presented.) is to restrict it to the case where there is only one susceptible class (Formula presented.), and when matrix B (given by the part of the new infection matrix, with respect to (Formula presented.)) is of rank one, with (Formula presented.). For this case, the first result we obtained was an explicit formula (12) for the replacement number (not surprisingly, accounting for varying demography, waning immunity and vaccinations led to several nontrivial modifications of the Arino et al. (2007) formula). The analysis of (Formula presented.) Arino–Brauer models is very challenging. As obtaining further general results seems very hard, we propose studying them at three levels: (A) the exact model, where only a few results are available—see Proposition 2;and (B) a "first approximation” (FA) of our model, which is related to the usually closed population model often studied in the literature. Notably, for this approximation, an associated renewal function is obtained in (7);this is related to the previous works of Breda, Diekmann, Graaf, Pugliese, Vermiglio, Champredon, Dushoff, and Earn. (C) Finally, we propose studying a second heuristic "intermediate approximation” (IA). Perhaps our main contribution is to draw attention to the importance of (Formula presented.) Arino–Brauer models and that the FA approximation is not the only way to tackle them. As for the practical importance of our results, this is evident, once we observe that the (Formula presented.) Arino–Brauer models include a large number of epidemic models (COVID, ILI, influenza, illnesses, etc.). © 2023 by the authors.
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In this paper, we investigate the effect of partially vaccinated and fully vaccinated individuals in pre-venting the transmit of COVID-19, especially in the regions of Tamil Nadu, Maharashtra, West Bengal and Delhi. Here we construct an SEIR model and analyse the behaviour. We obtained R0 by using next generation matrix approach. Also, our system shows two types of equilibria, namely disease free and endemic equilibrium. For both disease free and endemic equilibrium, local and global stability is obtained here. Our disease-free equilibrium is locally asymptotically stable whenever R0 is less than one, whereas the endemic equilibrium is locally asymptotically stable whenever R0 is greater than one. Furthermore, the global stability of disease-free equilibrium has been proven by using Lyapunov function and the global stability of endemic equilibrium has been obtained by using Poincare Bendixson technique. Also, we enhance our analytic results by numerical simulation. At the end we have attempted to fit our proposed model with the real-world data. © 2023 the author(s).
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In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples.
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In this paper we analyze COVID-19 spread in Indonesia using an epidemio logical model. We consider symptomatic and asymptomatic infections in the model. We analyze the equilibria of the model and their stability which depend on the basic reproduction ratio for symptomatic and asymptomatic infections. Furthermore, we use optimal control in prevention and treatment in decreasing the number of positive COVID-19 patients in Indonesia. Furthermore, we analyze the existence of optimal control using the Pontryagin minimum principle. We also give numerical simulation of COVID-19 spread with and without the control. According to the simulation, COVID-19 spread could be reduced by using prevention and treatment control simultaneously. © 2023 JONNER NAINGGOLAN et al.
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In the present work, we report a computational study on some important chemical properties of the flavonoid isorhamnetin, used in traditional medicine in many countries. In the course of the study we determined the acid-base equilibria in aqueous solution, the possible reaction pathways with the â¢OOH radical and the corresponding kinetic constants, the complexing capacity of copper ions, and the reduction of these complexes by reducing agents such as superoxide and ascorbic anion by using density functional level of theory Density Functional Theory. Finally, the non-covalent inhibition ability of the SARS-CoV-2 main protease enzyme by isorhamnetin was examined by molecular dynamics (MD) and docking investigation.
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In this paper we analyze COVID-19 spread in Indonesia using an epidemio logical model. We consider symptomatic and asymptomatic infections in the model. We analyze the equilibria of the model and their stability which depend on the basic reproduction ratio for symptomatic and asymptomatic infections. Furthermore, we use optimal control in prevention and treatment in decreasing the number of positive COVID-19 patients in Indonesia. Furthermore, we analyze the existence of optimal control using the Pontryagin minimum principle. We also give numerical simulation of COVID-19 spread with and without the control. According to the simulation, COVID-19 spread could be reduced by using prevention and treatment control simultaneously. © 2023 JONNER NAINGGOLAN et al.
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In this paper, a Covid-19 dynamical transmission model of a coupled non-linear fractional differential equation in the Atangana-Baleanu Caputo sense is proposed. The basic dynamical transmission features of the proposed system are briefly discussed. The qualitative as well as quantitative results on the existence and uniqueness of the solutions are evaluated through the fixed point theorem. The Ulam-Hyers stability analysis of the suggested system is established. The two-step Adams-Bashforth-Moulton (ABM) numerical method is employed to find its numerical solution. The numerical simulation is performed to accesses the impact of various biological parameters on the dynamics of Covid-19 disease.
Subject(s)
COVID-19 , Quarantine , Humans , Computer SimulationABSTRACT
The COVID-19 lockdowns have created a significant socioeconomic impact on our society. In this paper, we propose a population vaccination game framework, called EPROACH, to design policies for reopenings that guarantee post-opening public health safety. In our framework, a population of players decides whether to vaccinate based on the public and private information they receive. The reopening is captured by the switching of the game state. The insights obtained from our framework include the appropriate vaccination coverage threshold for safe-reopening and information-based methods to incentivize individual vaccination decisions. In particular, our framework bridges the modeling of the strategic behaviors of the populations and the spreading of infectious diseases. This integration enables finding the threshold which guarantees a disease-free epidemic steady state under the population's Nash equilibrium vaccination decisions. The equilibrium vaccination decisions depend on the information received by the agents. It makes the steady-state epidemic severity controllable through information. We find that the externalities created by reopening lead to the coordination of the players in the population and result in a unique Nash equilibrium. We use numerical experiments to corroborate the results and illustrate the design of public information for responsible reopening. © 2022 American Automatic Control Council.
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In this study, we have proposed a mathematical model to describe the dynamics of the spread of Middle East Respiratory Syndrome disease. The model consists of six-coupled ordinary differential equations. The existence of the corona-free equilibrium and endemic equilibrium points has been proved. The threshold condition for which the disease will die out or becomes permanent has been computed. That is the corona-free equilibrium point is locally asymptotically stable whenever the reproduction number is less than unity, and it is globally asymptotically stable (GAS) whenever the reproduction number is greater than unity. Moreover, we have proved that the endemic equilibrium point is GAS whenever the reproduction number is greater than unity. The results of the model analysis have been illustrated by numerical simulations.
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We analyze a mathematical model of COVID-19 transmission control, which includes the interactions among different groups of the population: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, based on a system of ordinary differential equations, which describes compartment model of a disease and its treatment. The aim of the model is to predict the development disease under different types of treatment during some fixed time period. We develop a game theoretic approach and a dual dynamic programming method to formulate optimal conditions of the treatment for an administration of a vaccine. Next, we calculate numerically an optimal treatment. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.
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In the absence of specific drugs and vaccines, the best way to control the spread of COVID-19 is to adopt and diligently implement effective and strict anti-epidemic measures. In this paper, a mathematical spread model is proposed based on strict epidemic prevention measures and the known spreading characteristics of COVID-19. The equilibria (disease-free equilibrium and endemic equilibrium) and the basic regenerative number of the model are analyzed. In particular, we prove the asymptotic stability of the equilibria, including locally and globally asymptotic stability. In order to validate the effectiveness of this model, it is used to simulate the spread of COVID-19 in Hubei Province of China for a period of time. The model parameters are estimated by the real data related to COVID-19 in Hubei. To further verify the model effectiveness, it is employed to simulate the spread of COVID-19 in Hunan Province of China. The mean relative error serves to measure the effect of fitting and simulations. Simulation results show that the model can accurately describe the spread dynamics of COVID-19. Sensitivity analysis of the parameters is also done to provide the basis for formulating prevention and control measures. According to the sensitivity analysis and corresponding simulations, it is found that the most effective non-pharmaceutical intervention measures for controlling COVID-19 are to reduce the contact rate of the population and increase the quarantine rate of infected individuals.
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It is well-known that methylene blue (MB),a cationic dye forms dimer and higher aggregates in aqueous solutions. For specific concentration range (1∙10−6–1∙10−4 M), a D⇌2M equilibria has been postulated and well characterized by visible electronic spectroscopy. The dye molecules can lead to formation of stacking (end on end and sandwich) type structures in solution phase stabilized by weak dispersion van der Waals forces and cation-anion-cation ion pairs and triplet interactions usually referred as hydrophobic interactions. Recent literature reports indicate that excess chemical potential of small hydrophobic particles and the strength of hydrophobic pair interactions appear to be linearly related. Our observations about precipitation of dye (MB) at higher concentrations of salt like sodium chloride (NaCl) made us to study the dimerization equilibria in detail since in the Corona health disaster;use of MB to diagnose the type of Covid variants helped Scientists in a great way. Salting-out of proteins is in general used to explain the specific protein aggregation behaviour observed in Huntington's disease. For model compound like tertiary butyl-alcohol, Geiger et al. reported enhancement of hydrophobic contacts which increase with increase in salt concentration. NaCl is an essential ingredient of biological fluids, of which concentration controls the various biological life governing processes. However, such information is non-existent for aqueous solutions of dyes. We therefore reported measured optical absorbance of aqueous solution containing NaCl (0.1–1.0 M) and dye at different concentrations (1∙10−6–1∙10−4 M) at 298 K spectrophotometrically, in the wavelength range of 550–700 nm. The spectrums are compared to those obtained for binary solutions of MB in water. Analysis of the spectral data yielded the dimer dissociation constant and individual characteristic monomer and dimer spectra. Further information about the geometry and twist angle between the dipoles of the MB molecules in the dimer species has been obtained. The results are analyzed for the monomer-dimer equilibria and salting-out effect as well applications of mass action model and exciton theories are discussed.
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The code sharing is the popular and effective cooperation of the airlines. First, this paper applies the spokes model to describe the different preferences of passengers for three airlines, and proposes the twostage game model and the simple method for the code sharing agreement choosing stage and the tickets' pricing stage under the free-sale model. Second, we use the numerical example to show the feasibility of the proposed models and method. By comparison and analysis, the Nash equilibrium situations of the two-stage game can be obtained. This study demonstrates: The code sharing agreement saves the total operating cost, but it raises the average airfare of the aviation market, so that the airlines' profits increase and the passengers' surpluses decrease;the government should promote the realization of better Nash equilibrium situation in order to maximize the total social welfare;to further improve the total social welfare during the period of Corona Virus Disease-19, the government could give the airlines some cost subsidies or adjust the passengers' psychological costs. Therefore, this paper provides significant theoretical and methodical supports to optimize the choices of the code sharing agreements and to improve the total social welfare in the aviation market. © 2022, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.
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This paper examines the impact of learning environments, educators’ attention, and students’ personal qualities on the outcomes of online learning. To approach conclusions, this paper describes the heterogeneous effect of these three types of factors on online learning outcomes and employs a fixed-effect regression to examine what exact factors constitute a good learning environment, appropriate educators’ attention and personal qualities that benefit students’ learning efficiency. The fixed-effect regression is applied on data of students’ answers to questionnaires and their final exam scores collected anonymously at three high schools in northern China during COVID-19 quarantine periods when Chinese high schools all conduct lessons and mid-term exams online but the final exam off-line, which is a major differentiation factor of this study. This paper contributes to three major findings: students who are more self-disciplined benefit more from the improvement of learning environments, practicing sports regularly improves online learning outcomes, and educators should find a balance between ensuring students are focused and not giving students too much pressure. © 2021 Association for Computing Machinery.
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We revisit here a landmark five-parameter SIR-type model, which is maybe the simplest example where a complete picture of all cases, including non-trivial bistability behavior, may be obtained using simple tools. We also generalize it by adding essential vaccination and vaccination-induced death parameters, with the aim of revealing the role of vaccination and its possible failure. The main result is Theorem 1, which describes the stability behavior of our model in all possible cases.
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Deferoxamine B is an outstanding molecule which has been widely studied in the past decade for its ability to bind iron and many other metal ions. The versatility of this metal chelator makes it suitable for a number of medicinal and analytical applications, from the well-known iron chelation therapy to the most recent use in sensor devices. The three bidentate hydroxamic functional groups of deferoxamine B are the centerpiece of its metal binding ability, which allows the formation of stable complexes with many transition, lanthanoid and actinoid metal ions. In addition to the ferric ion, in fact, more than 20 different metal complexes of deferoxamine b have been characterized in terms of their chemical speciation in solution. In addition, the availability of a terminal amino group, most often not involved in complexation, opens the way to deferoxamine B modification and functionalization. This review aims to collect and summarize the available data concerning the complex-formation equilibria in solutions of deferoxamine B with different metal ions. A general overview of the progress of its applications over the past decade is also discussed, including the treatment of iron overload-associated diseases, its clinical use against cancer and neurodegenerative disorders and its role as a diagnostic tool.