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Throughout history, infectious diseases have been the cause of outbreaks and the deaths of people. It is crucial for endemic disease management to be able to forecast the number of infections at a given moment and the frequency of new infections so that the appropriate precautions can be taken. The COVID-19 pandemic has highlighted the value of mathematical modeling of pandemics. The susceptible–infected–quarantined–recovered–vaccinated (SIQRV) epidemic model was used in this work. Symmetrical aspects of the proposed dynamic model, disease-free equilibrium, and stability were analyzed. The symmetry of the population size over time allows the model to find stable equilibrium points for any parameter value and initial conditions. The assumption of the strong symmetry of the initial conditions and parameter values plays a key role in the analysis of the fractional SIQRV model. In order to combat the pandemic nature of the disease, control the disease in the population, and increase the possibility of eradicating the disease, effective control measures include quarantine and immunization. Fractional derivatives are used in the Caputo sense. In the model, vaccination and quarantine are two important applications for managing the spread of the pandemic. Although some of the individuals who were vaccinated with the same type and equal dose of vaccine gained strong immunity thanks to the vaccine, the vaccine could not give sufficient immunity to the other part of the population. This is thought to be related the structural characteristics of individuals. Thus, although some of the individuals vaccinated with the same strategy are protected against the virus for a long time, others may become infected soon after vaccination. Appropriate parameters were used in the model to reflect this situation. In order to validate the model, the model was run by taking the COVID-19 data of Türkiye about a year ago, and the official data on the date of this study were successfully obtained. In addition to the stability analysis of the model, numerical solutions were obtained using the fractional Euler method. © 2023 by the authors.
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As tuberculosis (TB) patients do not have lifetime immunity, environmental transmission is one of the key reasons why TB has not been entirely eradicated. In this study, an SVEIRB model of recurrent TB considering environmental transmission was developed to explore the transmission kinetics of recurrent TB in the setting of environmental transmission, exogenous infection, and prophylaxis. A more thorough explanation of the effect of environmental transmission on recurrent TB can be found in the model's underlying regeneration numbers. The global stability of disease-free and local equilibrium points can be discussed by looking at the relevant characteristic equations. The Lyapunov functions and the LaSalle invariance principle are used to show that the local equilibrium point is globally stable, and TB will persist if the basic reproduction number is larger. Conversely, the disease will disappear if the basic reproduction number is less than one. The impact of environmental transmission on the spread of tuberculosis was further demonstrated by numerical simulations, which also demonstrated that vaccination and reducing the presence of the virus in the environment are both efficient approaches to control the disease's spread.
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In the context of vaccination, we develop a novel mathematical model to examine the Omicron type of coronavirus illness. The system's mathematical analysis based on its equilibrium points shall be obtained. The threshold quantity is used to investigate the system's local and global asymptotical analysis. The Omicron vaccination model shown to be stable locally asymptotically if R 0 v < 1 . The system is globally asymptotically stable at the disease-free equilibrium for a special case when η = 1 if R 0 v < 1 . We estimate the model parameters based on the observed data and show that the threshold is R 0 ≈ 2.4894 in the absence of vaccination. The model has the phenomenon of backward bifurcation under certain conditions. Herd immunity analysis is obtained and it turns out that the herd immunity threshold for the South African population is 74%. The impact of vaccination on disease dynamics is also shown and discussed. Further, we have given some graphical results showing the community's disease reduction. [ FROM AUTHOR] Copyright of Waves in Random & Complex Media is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)
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Severe acute respiratory syndrome coronavirus is a type 2 highly contagious, and transmissible among humans;the natural human immune response to severe acute respiratory syndrome-coronavirus-2 combines cell-mediated immunity (lymphocyte) and antibody production. In the present study, we analyzed the dynamic effects of adaptive immune system cell activation in the human host. The methodology consisted of modeling using a system of ordinary differential equations;for this model, the equilibrium free of viral infection was obtained, and its local stability was determined. Analysis of the model revealed that lymphocyte activation leads to total pathogen elimination by specific recognition of viral antigens;the model dynamics are driven by the interaction between respiratory epithelial cells, viral infection, and activation of helper T, cytotoxic T, and B lymphocytes. Numerical simulations showed that the model solutions match the dynamics involved in the role of lymphocytes in preventing new infections and stopping the viral spread;these results reinforce the understanding of the cellular immune mechanisms and processes of the organism against severe acute respiratory syndrome-coronavirus-2 infection, allowing the understanding of biophysical processes that occur in living systems, dealing with the exchange of information at the cellular level.
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In the present paper, a mathematical model using the non-linear differential equations depicting the impact of Covid-19 on unemployment is discussed. The stability of the system is studied and model is reformulated as an optimal control problem. To assess the impact of unemployment on human population, two time-dependent controls are used. Providing education and training of job-oriented persons act as first control and campaigning about the awareness of coronavirus disease and self-employment business is the second control. Necessary conditions for optimal control are derived by Pontryagins maximum principle. Further, the results are illustrated by numerical simulation.
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INTRODUCTION: Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. OBJECTIVES: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. METHODS: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. RESULTS: Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. CONCLUSION: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.
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The concept and practicalities of sustainable business development attract increasing interest of general public, companies, legislators, activists, academics and many others. Our understanding of what constitutes sustainability is evolving, especially nowadays when the pandemic and digitalization caused major shifts globally. In such conditions, it is no wonder that managers and business owners may face difficulties in implementation and evaluation of sustainable practices. Therefore, The objective: of the paper is to examine theoretical foundations of the concept of business sustainability and propose an up-to-date model for its appraisal. The paper is divided into two primary parts in addition to introduction and conclusion. The first part is dedicated to the examination of the terms 'stability' and 'sustainability' universally and in business environment. The second part includes description of our suggested evaluation model of economic, social and environmental sustainability perspectives using relevant indicators. Methods/Analysis: the research includes review of academic literature and empirical research on the topic of business sustainability and analytical consolidation of existing approaches to its appraisal. Findings: theoretical contribution to perception and development of the conditions of business stability and sustainability, and evaluation model including specific indicators across the three primary sustainability directions. Application/Improvements: the research is useful to general public, but is of special interest to business leaders interested in implementation of sustainable practices.
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Efficacy of the healthcare system and illumination (awareness) activities control COVID-19. To defend public health, the spreading pandemic of COVID-19 disease necessitates social distancing, wearing masks, personal cleanliness, and precautions. Due to inadequate awareness programs, COVID-19 rapidly increases in India. The primary goal of this research is to investigate the spreading behavior of the COVID-19 virus in India when people are aware of the disease. We find the optimum value of disease transmission rate and detection of the unidentified asymptomatic and symptomatic populations. An optimal control problem is designed with limited resource allocation to improve the recovered individuals. A stability analysis presents for emphasizes the relevance of disease awareness in preventing the spread of the disease. The control parameters are used to explore the increase and decrease of the infected individual with and without control in optimal control analysis. The model is simulated using the Hattaf-fractional derivative to study the memory effect in the epidemic. To adapt the model to the total number of reported COVID-19 cases in India, we collected data from March 20, 2021 to September 30, 2021. According to the simulation results, the pandemic would spread faster if awareness campaigns were improperly carried out.
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In this paper, the effect of contaminated objects on a SIRS Model with vaccination and hospitalization compartments is modeled. Positivity and boundedness properties of the solutions of model are proved, basic reproduction number of the model is founded through criteria which make the eigenvalues of the Jacobean matrix at the disease-free equilibrium point, negative. Globally stability analysis of the disease-free equilibrium point is proved when the basic reproduction number is less than unity. The existence, uniqueness of the endemic equilibrium point is investigated when the basic reproduction number is greater than unity. Parameter values regarding to spreading covid-19 in Kurdistan region are estimated. Finally, sensitivity analysis of the reproduction number is carried out. © 2022 Production by the University of Garmian. This is an open access article under the LICENSE.
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Objective To develop a novel gold immunochromatographic double antibody sandwich assay for the detection of SARS-CoV-2 antigen, and to evaluate the performance of major reagents. Methods Potassium carbonate, large colloidal gold and SARS-CoV-2 antibody were used to prepare colloidal gold antibody markers, SARS-CoV-2 antibody concentration was optimized to prepare the binding pad, SARS-CoV-2 antibody and goat anti-mouse IgG were coated on nitrocellulose membrane as detection line and quality control line, according to the process requirements to assembly the assay. The minimum detection limit, cross-reactivity, accelerated stability test and clinical evaluation of the antigen detection reagent were determined. Results The minimum detection limit of SARS-CoV-2 inactivated virus was 3. 3×10~2 TCID50/ml, and no cross-reaction was found in the samples containing 10 common pathogens. The results of 37 °C high temperature accelerated test for 28 d showed high stability of the reagent. The sensitivity, specificity and total coincidence rate were 92. 00%, 100. 00% and 98. 67% and the Kappa value of concordance test was 0. 939, P＜0. 01. Conclusion The developed antigen detection assay has high sensitivity and specificity, which is also simple to operate in a short time. It can be used as a rapid detection method for large-scale screening of novel coronavirus.
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During the COVID-19 pandemic, panic buying, price inflation, and the pollution of production processes led to economic and social unrest. In response to the current situation, the current research takes less account of the subjective perception of public panic buying and the lack of reference to the reality of effective governance. First, this paper uses prospect theory to portray the public's perceived value of goods in panic buying and non-panic buying situations. Then, drawing on the experience of effective governance in China, a tripartite evolutionary game model of local government, the public and green smart supply chain enterprises is constructed under the reward and punishment mechanism of the central government. Then, this paper analyzes the strategic choices of each game player and the stability of the system equilibrium. The structure of the study suggests the following. (1) Improving local government subsidies and penalties, the cost of positive response and the probability of response can lead to an evolutionary direction where the public chooses not to panic buy and green smart supply chain enterprises choose to ensure a balance between supply and demand and increase pollution control in the production process. (2) Our study yields three effective combinations of evolutionary strategies, of which an ideal combination of evolutionary strategies exists. Non-ideal evolutionary strategy combinations can occur due to improper incentives and penalties of local governments and misallocation of limited resources. However, we find four paths that can transform the non-ideal evolutionary strategy combination into an ideal evolutionary strategy combination. (3) The central government's reward and punishment mechanism is an important tool to stabilize the tripartite strategy, but the central government cannot achieve effective governance by replacing incentives with punishment.
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Information is important market resource. High-quality information is beneficial to increase enterprise's reputation and reduce consumer's verification cost. This paper constructs a two-layer dynamic model, in which enterprises simultaneously conduct price and information game. The goal of profit maximization integrates two types of games into one system. The complex evolution of the two-layer system are studied by equilibrium analysis, stability analysis, bifurcation diagram, entropy and Lyapunov exponent. It is found that improving the information quality through regulations will increase involution and reduce stability of the market. Then, the block chain technology is introduced into the model for improving information quality of the market. It is found that increasing enterprises' willingness to adopt block chain can improve the information quality quickly and effectively, and that is verified by entropy value. Therefore, the application and promotion of new technologies are more effective than exogenous regulations for improving information quality in market.
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Objective To compare the performance of two qPCR instruments in detecting SARS-CoV-2 virus in the nasopharyngeal swab samples of suspected COVID-19 isolated individuals in Jinghu district Wuhu city.Methods A total of 151 nasopharyngeal swab samples were collected from individuals with suspected COVID-19isolated during January 2021 and July 2022 at a quarantine site in the Jinghu district. Nucleic acid of SARS-CoV-2virus was quantified parallelly using ABIQ5 real-time fluorescence quantitative analyzer（Q5 analyzer） and Bole CFX96 fluorescence quantitative PCR analyzer（Bole analyzer） in the laboratory. Q5 analyzer was used as the reference instrument, while Bole analyzer was used as an experimental instrument. The detection results of N gene, ORF1ab fragment and CT value of the two RT-PCR machines were analyzed and compared using paired four grid test, Spearman test and paired sample t-test in SPSS 22 statistical software. Results The results of 151samples for different target genes tested by two instruments were in good agreement（N gene: Kappa=1, P＜0. 05;ORF1ab fragment: Kappa=0. 972, P＜0. 05）. The inter-batch repeatability rates were 4. 01% and 3. 04%for N gene and ORF fragment of the same batch positive quality controls by Q5 analyzer, and were 4. 90% and 3. 57% by Bole analyzer. The intra batch repeatability rates of the two instruments at different hole locations were similar, and CV values were less than 3%. The results of 23 positive samples showed that the differences in CT values of N gene（29. 38±7. 22） and ORF1ab（30. 83±6. 27） detected by Q5 analyzer were statistically significant（t=2. 765, P＜0. 05）, while the differences in CT values of N gene（29. 58±7. 27） and ORF1ab（30. 77±8. 02） detected by Bole analyzer were not statistically significant（t=1. 753, P＞0. 05）. The correlation coefficients of CT values of different target genes detected by the two instruments were rN=0. 960 and rORF=0. 865, showing correlated CT values（P＜0. 05）. Conclusion The CT values of N gene and ORF1ab fragment of SARS-CoV-2 virus detected by the two instruments have strong correlation and agreement, indicating that either of the instrument can be used for laboratory sample detection and analysis. The repeatability of Q5 analyzer is better than that of Bole analyzer. The detection stability of ORF fragments of both instruments is better than that of N gene, and the detection sensitivity of Q5 analyzer for N gene is higher than that for ORF fragment. The sample tubes should be placed in the middle of the PCR machine in order to reduce the system error.
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In this paper, we develop and analyse a modified susceptible-infected-recovered (SIR) compartment model by integrating the vaccination factor as a model parameter to investigate the effect of vaccination parameter on the long-term outcomes of the COVID-19 pandemic. Mathematical analysis is used to determine the disease-free equilibrium, the endemic equilibrium, and the basic reproduction number of the developed model. The stability of the model is studied using the Routh-Hurwitz criterion, and numerical simulations are conducted to assess the impact of vaccination on the disease at different rates. The findings suggest that vaccination rate influences the transmission dynamics, and the vaccine can speed up the COVID-19 recovery and contain the outbreak. © 2023 Inderscience Enterprises Ltd.
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Bank Indonesia, el banco central de Indonesia, ha realizado ajustes en un instrumento de política macroprudencial llamado índice de intermediación macroprudencial (IIM) para impulsar el crecimiento de los préstamos en el contexto de la recuperación económica nacional debido a la pandemia de COVID-19. En este artículo, se desarrolla un modelo dinámico de préstamo bancario con comportamiento procíclico, y se equipa con el instrumento predecesor del IIM denominado requerimiento de reserva basado en la relación préstamo-depósito (RR-RPD). Examinamos los efectos de los parámetros RR-RPD en la dinámica del préstamo utilizando el análisis de bifurcación de colisión de fronteras para determinar los valores umbral de los parámetros RR-RPD para que se pueda mantener la estabilidad del equilibrio del préstamo. Este modelo se aplica a los datos mensuales de los bancos comerciales de Indonesia antes y durante la pandemia de COVID-19 para evaluar la región de estabilidad de los parámetros del instrumento.Alternate :Bank Indonesia, the central bank of Indonesia, has made adjustment settings in a macroprudential policy instrument called macroprudential intermediation ratio (MIR) to boost loan growth in the context of national economic recovery due to the COVID-19 pandemic. In this paper, a dynamic model of bank loan with procyclicality behavior is developed, and it is equipped with the predecessor of the MIR instrument called loan-to-deposit ratio based reserve requirement (LDR-RR). We examine the effects of LDR-RR parameters on the dynamics of loan using the border collision bifurcation analysis to determine the threshold values of the LDR-RR parameters so that the stability of loan equilibrium can be maintained. This model is applied to monthly data of Indonesian commercial banks before and during the COVID-19 pandemic to assess the stability region of the instrument parameters.
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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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Due to the interaction of electric multiple units (EMUs), and the electric traction networks, low frequency oscillations (LFOs) appear leading to traction blockade and overall stability related issues. For suppressing LFOs, coronavirus herd immunity optimiser (CHIO), a recently developed meta-heuristic, has been applied for tuning controller parameters. Controller parameters are tuned to minimise the integral time absolute error (ITAE) that regulates DC-link capacitor voltage. Results obtained using CHIO are compared with those found using other well-established algorithms like symbiotic organisms search (SOS) and particle swarm optimisation (PSO). The supremacy of CHIO over other mentioned algorithms for mitigating LFOs was demonstrated for a diverse range of operating conditions. Results demonstrates that overshoot for the proposed algorithm-based traction unit is 1.0061% whereas those for SOS and PSO based algorithm are obtained as 6.4542 % and 20.6166%, respectively which are quite high. CHIO is more stable than SOS and PSO and requires settling time of 0.1934 s only to reach steady-state condition, which is 50.21% faster than SOS and 65.03% faster than PSO. Also, the total harmonic distortion (THD) for line currents of the secondary side of traction transformer (TT) are obtained as 0.88%, 2.17%, and 12.48% for CHIO, SOS, and PSO, respectively.
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We develop a complex network-based SIS q I q RS model, calculate the threshold R 0 of infectious disease transmission and analyze the stability of the model. In the model, three control measures including isolation and vaccination are considered, where the isolation is structured in isolation of susceptible nodes and the isolation of infected nodes. We regard these three kinds of controls as time-varying variables, and obtain the existence and the solution of the optimal control by using the optimal control theory. With regard to the stability of the model, sensitivity analysis of the parameters and optimal control, we carry out numerical simulations. From the simulation results, it is obvious that when the three kinds of controls exist simultaneously, the scale and cost of the disease are minimal. Finally, we fit the real data of COVID-19 to the numerical solution of the model.
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A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and indirect mode of transmission), existence and uniqueness, as well as stability analysis of the solution of the model, are studied. The paper studies the effect of optimal control policy applied to shedding effect. The control is the observation of standard hygiene practices and chemical disinfectants in public spaces. Numerical simulations are carried out to support the analytic result and to show the significance of the fractional order from the biological viewpoint.
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In this article, Euler's technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the system under consideration that serves as an example of the investment model. The mathematical investment model consists of a system of four fractional-order nonlinear differential equations of the generalized Liouville–Caputo type. Moreover, the existence and uniqueness of solutions for the above fractional order model under pandemic situations were investigated using the well-known Schauder and Banach fixed-point theorem technique. The stability analysis in the context of Ulam—Hyers and generalized Ulam—Hyers criteria was also discussed. Using the investment model under consideration, a new analysis was conducted. Figures that depict the behavior of the classes of the projected model were used to discuss the obtained results. The demonstrated results of the employed technique are extremely emphatic and simple to apply to the system of non-linear equations. When a generalized Liouville–Caputo fractional derivative parameter (ρ) is changed, the results are asymmetric. The current work can attest to the novel generalized Caputo-type fractional operator's suitability for use in mathematical epidemiology and real-world problems towards the future pandemic circumstances.