ABSTRACT
After the outbreak of COVID-19, it is of great significance to find an appropriate dynamic model of COVID-19 epidemic in order to master its transmission law, predict its development trend, and provide corresponding prevention and control basis. In this paper, the SEIRV chamber model is adopted, and the dynamics model of infectious disease is established by combining the fractional derivative of Conformable. The fractional derivative differential equation of Conformable is discretized by numerical method and its numerical solution is obtained. In addition, numerical simulation was carried out on the confirmed data of Wuhan city from January 23, 2020 to February 11, 2020. At the same time, consider that the Wuhan municipal government revised the epidemic data on February 12, 2020, adding nearly 14,000 people. The order α value of SEIRV model is modified, and then the revised data is simulated. The simulation results are in good agreement with the published data. The results show that compared with the traditional integer order model, the fractional order model can simulate the modified data. This reflects the advantages of fractional infectious disease dynamics model, and can provide certain reference value for the prediction of COVID-19 model. © 2022 Editorial Borad of Complex Systems and Complexity Science. All rights reserved.
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Humanity is currently living a true nightmare never seen before due to the pandemic caused by COVID-19 disease, scientific researchers are working day and night to find an ideal vaccine that eradicates this pandemic. The purpose of this paper is to investigate a SIHV pandemic model taking into account a vaccination strategy. For this aim, we consider a model with four compartments that describes the interaction between the susceptible cases S, the real infected cases I, the hospitalized, confirmed infected cases H and the vaccinated-treated individuals V. We establish the local stability of our model, depending on the basic reproduction number, by using the Routh-Hurwitz theorem. We perform some numerical simulations in order to confirm our theoretical results and discuss the effect of the rate of vaccination on controlling the spread of COVID-19. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022.
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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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Respirators provide protection from inhalation exposure to dangerous substances, such as chemicals and infectious particles, including SARS-COVID-laden droplets and aerosols. However, they are prone to exposure to stale air as masks create a microclimate influenced by the exhaled air. As a result, exhaled air from lungs accumulating in the mask produces a warm and humid environment that has a high concentration of carbon dioxide (CO2), unsuitable for re-inhalation. Fans are a favorable option for respirators to ventilate the mask and remove the stale air. This study utilized computational fluid dynamics simulation consisting of a hybrid Reynolds-averaged Navier-Stokes-large eddy simulation turbulence method to compare the inhalation flow properties for different fan locations (bottom, top, and side) with regular respirator breathing. Three mask positions, top, side, and bottom, were evaluated under two breathing cycles (approximately 9.65 s of breathing time). The results demonstrated that adding a fan respirator significantly decreased internal mask temperature, humidity, and CO2 concentration. The average CO2 concentration decreased by 87%, 67%, and 73% for locations bottom, top, and side, respectively. While the top and side fan locations enhanced the removal of the exhaled gas mixture, the bottom-fan respirator was more efficient in removing the nostril jet gas mixture and therefore provided the least barrier to respiratory function. The results provide valuable insight into the benefits of fan respirators for long-term use for reducing CO2 concentration, mask temperature, and humidity, improving wearer safety and comfort in hazardous environments, especially during the COVID-19 pandemic.
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The COVID-19 pandemic has had a significant impact on the global population, with millions of cases and deaths reported worldwide. In this study, we use mathematical models to analyze the spread of the disease, with a focus on careless infective models. We develop and analyze mathematical models to understand the transmission dynamics of COVID-19, taking into account the impact of human behavior, such as the spread of the disease by individuals who are unaware that they are infected. Our results provide insights into the role of careless infective individuals in the spread of the disease and suggest the need for targeted interventions to reduce the impact of COVID-19 The results of this study contribute to a better understanding of the spread of COVID-19 and inform public health measures to control its transmission. © 2023 Asia Pacific Journal of Mathematics.
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The COVID-19 pandemic has demonstrated the demand for more effective procedures for sanitizing environments, especially high-risk ones, such as hospitals. Several products are used as disinfectants, with ozone being one of the strongest oxidants known. High relative humidity helps reduce the contact time required for viruses and bacteria inactivation with ozone. Thus, this work aimed to analyze the dispersion of an ozonized mist by CFD simulation to sanitize a hospital operating room. To our best knowledge, for the first time, the dispersion of an ozonized mist was investigated by CFD. The mathematical and numerical models were validated with results from the literature. The decay kinetics of the ozonized mist was obtained experimentally, resulting in a first order reaction with a kinetic constant of 2.66 × 10−4 s−1. The numerical results of concentration on the surfaces were analyzed qualitatively and quantitatively, providing relevant information about the fluid dynamics of the sanitizing process. Ozone mist concentrations were higher on the walls close to the generator and lower on the furthest walls and the ceiling. The ozone mist concentration in the room reached an average of 11 mg/L. Five minutes of ozone mist generation and another five minutes of decay by air circulation were sufficient to provide an increase in ozone mist to concentrations above 4 mg/L, considered satisfactory for the sanitization of the operating room surfaces. [ FROM AUTHOR] Copyright of Ozone: Science & Engineering 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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The ensuing study analyzes the trend of disinformation appertaining to the coronavirus pandemic on social media platforms through mathematical modeling. We introduce a new SEHIR model with an additional compartment of people not reacting instantly or at all to the disinformation called hibernators, to obtain more clarity on the pattern of spread of fake news. The stability analyses of the prevalence free equilibrium have been provided in terms of basic reproduction number, and the existence and uniqueness of the solution have been proved using the fixed-point technique. Furthermore, we conduct a numerical simulation using an experimental survey. The findings are graphically depicted to show different scenarios for social media users across compartments.
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The coronavirus infectious disease (or COVID-19) is a severe respiratory illness. Although the infection incidence decreased significantly, still it remains a major panic for human health and the global economy. The spatial movement of the population from one region to another remains one of the major causes of the spread of the infection. In the literature, most of the COVID-19 models have been constructed with only temporal effects. In this paper, a vaccinated spatio-temporal COVID-19 mathematical model is developed to study the impact of vaccines and other interventions on the disease dynamics in a spatially heterogeneous environment. Initially, some of the basic mathematical properties including existence, uniqueness, positivity, and boundedness of the diffusive vaccinated models are analyzed. The model equilibria and the basic reproductive number are presented. Further, based upon the uniform and non-uniform initial conditions, the spatio-temporal COVID-19 mathematical model is solved numerically using finite difference operator-splitting scheme. Furthermore, detailed simulation results are presented in order to visualize the impact of vaccination and other model key parameters with and without diffusion on the pandemic incidence. The obtained results reveal that the suggested intervention with diffusion has a significant impact on the disease dynamics and its control.
Subject(s)
COVID-19 , Humans , COVID-19/epidemiology , COVID-19/prevention & control , Vaccination , Pandemics/prevention & control , Basic Reproduction Number , Computer SimulationABSTRACT
When an individual with confirmed or suspected COVID-19 is quarantined or isolated, the virus can linger for up to an hour in the air. We developed a mathematical model for COVID-19 by adding the point where a person becomes infectious and begins to show symptoms of COVID-19 after being exposed to an infected environment or the surrounding air. It was proven that the proposed stochastic COVID-19 model is biologically well-justifiable by showing the existence, uniqueness, and positivity of the solution. We also explored the model for a unique global solution and derived the necessary conditions for the persistence and extinction of the COVID-19 epidemic. For the persistence of the disease, we observed that Rs0>1, and it was noticed that, for Rs<1, the COVID-19 infection will tend to eliminate itself from the population. Supplementary graphs representing the solutions of the model were produced to justify the obtained results based on the analysis. This study has the potential to establish a strong theoretical basis for the understanding of infectious diseases that re-emerge frequently. Our work was also intended to provide general techniques for developing the Lyapunov functions that will help the readers explore the stationary distribution of stochastic models having perturbations of the nonlinear type in particular.
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The deadly coronavirus disease 2019 (COVID-19) has recently affected each corner of the world. Many governments of different countries have imposed strict measures in order to reduce the severity of the infection. In this present paper, we will study a mathematical model describing COVID-19 dynamics taking into account the government action and the individuals reaction. To this end, we will suggest a system of seven fractional deferential equations (FDEs) that describe the interaction between the classical susceptible, exposed, infectious, and removed (SEIR) individuals along with the government action and individual reaction involvement. Both human-to-human and zoonotic transmissions are considered in the model. The well-posedness of the FDEs model is established in terms of existence, positivity, and boundedness. The basic reproduction number (BRN) is found via the new generation matrix method. Different numerical simulations were carried out by taking into account real reported data from Wuhan, China. It was shown that the governmental action and the individuals' risk awareness reduce effectively the infection spread. Moreover, it was established that with the fractional derivative, the infection converges more quickly to its steady state.
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In this paper, a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed. Firstly, the existence and uniqueness of the global positive solution is obtained. Secondly, threshold criteria for the stochastic extinction and persistence in the mean with probability one are established. Moreover, a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established. Finally, numerical simulations are carried out in combination with real COVID-19 data from Urumqi, China and the theoretical results are verified.
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These days the online social network has become a huge source of data. People are actively sharing information on these platforms. The data on online social networks can be misinformation, information, and disinformation. Because online social networks have become an important part of our lives, the information on online social networks makes a great impact on us. Here a differential epidemic model for information, misinformation, and disinformation on online social networks is proposed. The expression for basic reproduction number has been developed. Again, the stability condition for the system at both infection-free and endemic equilibriums points has been discussed. The numerical simulation has been performed to validate the theoretical results. Data available on Twitter related to COVID-19 vaccination is used to perform the experiment. Finally, the authors discuss the control strategy to minimize the misinformation and disinformation related to vaccination. © 2022 Authors. All rights reserved.
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On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy. The SARS-COV-2 virus has spread throughout the Kingdom of Morocco. In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco. By sup-porting a SIW IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study. Our main goal is to characterize the optimum order of control-ling the spread of the COVID-19 pandemic by adopting a vaccination strategy, the aim of which is to reduce the number of susceptible and infected individuals without vaccination and to maximize the recovered individuals by reducing the cost of vaccination using one of the vaccines approved by the World Health Organization. To do this, we proved the existence of a pair of control. It provides a description of the optimal controls in terms of state and auxiliary functions. Finally, we provided numerical simulations of data related to the transmission of the COVID-19 pandemic. Numerical results are presented to illustrate the effectiveness of the adopted approach. ©2023 Lviv Polytechnic National University.
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Medical treatment, vaccination, and quarantine are the most efficacious controls in preventing the spread of contagious epidemics such as COVID-19. In this paper, we demonstrate the global stability of the endemic and disease-free equilibrium by using the Lyapunov function. Moreover, we apply the three measures to minimize the density of infected people and also reduce the cost of controls. Furthermore, we use the Pontryagin Minimum Principle in order to characterize the optimal controls. Finally, we execute some numerical simulations to approve and verify our theoretical results using the fourth order Runge-Kutta approximation through Matlab. © 2023 the author(s).
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In this study, we have proposed and analyzed a new COVID-19 and syphilis co-infection mathematical model with 10 distinct classes of the human population (COVID-19 protected, syphilis protected, susceptible, COVID-19 infected, COVID-19 isolated with treatment, syphilis asymptomatic infected, syphilis symptomatic infected, syphilis treated, COVID-19 and syphilis co-infected, and COVID-19 and syphilis treated) that describes COVID-19 and syphilis co-dynamics. We have calculated all the disease-free and endemic equilibrium points of single infection and co-infection models. The basic reproduction numbers of COVID-19, syphilis, and COVID-19 and syphilis co-infection models were determined. The results of the model analyses show that the COVID-19 and syphilis co-infection spread is under control whenever its basic reproduction number is less than unity. Moreover, whenever the co-infection basic reproduction number is greater than unity, COVID-19 and syphilis co-infection propagates throughout the community. The numerical simulations performed by MATLAB code using the ode45 solver justified the qualitative results of the proposed model. Moreover, both the qualitative and numerical analysis findings of the study have shown that protections and treatments have fundamental effects on COVID-19 and syphilis co-dynamic disease transmission prevention and control in the community. Copyright © 2023 Teklu and Terefe.
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The rapid emergence of the coronavirus disease 2019 (COVID-19) has already taken on pandemic proportions, resulting thousands of deaths around the world. In the present manuscript, a mathematical model is proposed to investigate the current outbreak of the COVID-19. The model includes multiple transmission pathways and emphasises the role of asymptomatic and symptomatic infected population in the spread of this disease. To predict upcoming situation and a detail analysis of the spread of COVID-19 outbreak, basic reproduction number is calculated using publicly reported data from three different countries, where the outbreak is at its peak (USA), initial level (India) and controlled up to certain level (Japan). Analytical and numerical results of the model indicate that current on-going outbreak of COVID-19 would remain endemic if we do not proceed with extreme vigilance due to the serious risk it poses around the globe.
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In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan city of China. This virus has attracted worldwide attention and spreads rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we investigate an incommensurate fractional-order SIQR (susceptible, infectious, quarantined, and removed) for modeling COVID-19 by considering a nonlinear saturated incidence rate within the scope of the so-called Atangana-Baleanu fractional derivatives. We prove the existence and uniqueness of the solutions for the proposed model using a standard fixed point theorem. We present and discuss the equilibria of the studied model (disease-free and endemic equilibria). We also carry out some numerical simulations using the Euler method to support the theoretical findings. Moreover, we estimate the value of the fractional derivation orders and the parameters for studying the model using a machine learning algorithm. Furthermore, we perform the sensitivity analysis of the parameter. As a result, our proposed model is in good agreement with the given real data of COVID-19. © 2023 Elsevier Inc. All rights reserved.
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In this study, we formulated a mathematical model of COVID-19 with the effects of partially and fully vaccinated individuals. Here, the purpose of this study is to solve the model using some numerical methods. It is complex to solve four equations of the SEIR model, so we introduce the Euler and the fourth-order Runge–Kutta method to solve the model. These two methods are efficient and practically well suited for solving initial value problems. Therefore, we formulated a simple nonlinear SEIR model with the incorporation of partially and fully vaccinated parameters. Then, we try to solve our model by transforming our equations into the Euler and Runge–Kutta methods. Here, we not only study the comparison of these two methods, also found out the differences in solutions between the two methods. Furthermore, to make our model more realistic, we considered the capital of Kerala, Trivandrum city for the simulation. We used MATLAB software for simulation purpose. At last, we discuss the numerical comparison between these two methods with real world data. Copyright © 2023 M, C and Al-Mdallal.
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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).
ABSTRACT
The global spread of COVID-19 has not been effectively controlled. It poses a significant threat to public health and global economic development. This paper uses a mathematical model with vaccination and isolation treatment to study the transmission dynamics of COVID-19. In this paper, some basic properties of the model are analyzed. The control reproduction number of the model is calculated and the stability of the disease-free and endemic equilibria is analyzed. The parameters of the model are obtained by fitting the number of cases that were detected as positive for the virus, dead, and recovered between January 20 and June 20, 2021, in Italy. We found that vaccination better controlled the number of symptomatic infections. A sensitivity analysis of the control reproduction number has been performed. Numerical simulations demonstrate that reducing the contact rate of the population and increasing the isolation rate of the population are effective non-pharmaceutical control measures. We found that if the isolation rate of the population is reduced, a short-term decrease in the number of isolated individuals can lead to the disease not being controlled at a later stage. The analysis and simulations in this paper may provide some helpful suggestions for preventing and controlling COVID-19.