Nonlinear dynamics modeling and epidemic forecast of COVID-19

To study the spreading trend and risk of COVID-19, according to the characteristics of COVID-19, this paper proposes a new transmission dynamic model named SLIR(susceptible-low-risk-infected-recovered), based on the classic SIR model by considering government control and personal protection measures. The equilibria, stability and bifurcation of the model are analyzed to reveal the propagation mechanism of COVID-19. In order to improve the prediction accuracy of the model, the least square method is employed to estimate the model parameters based on the real data of COVID-19 in the United States. Finally, the model is used to predict and analyze COVID-19 in the United States. The simulation results show that compared with the traditional SIR model, this model can better predict the spreading trend of COVID-19 in the United States, and the actual official data has further verified its effectiveness. The proposed model can effectively simulate the spreading of COVID-19 and help governments choose appropriate prevention and control measures. Copyright ©2023 Control and Decision.

A Mathematical Study for the Transmission of Coronavirus Disease

Globally, the COVID-19 pandemic's development has presented significant societal and economic challenges. The carriers of COVID-19 transmission have also been identified as asymptomatic infected people. Yet, most epidemic models do not consider their impact when accounting for the disease's indirect transmission. This study suggested and investigated a mathematical model replicating the spread of coronavirus disease among asymptomatic infected people. A study was conducted on every aspect of the system's solution. The equilibrium points and the basic reproduction number were computed. The endemic equilibrium point and the disease-free equilibrium point had both undergone local stability analyses. A geometric technique was used to look into the global dynamics of the endemic point, whereas the Castillo-Chavez theorem was used to look into the global stability of the disease-free point. The system's transcritical bifurcation at the disease-free point was discovered to exist. The system parameters were changed using the basic reproduction number's sensitivity technique. Ultimately, a numerical simulation was used to apply the model to the population of Iraq in order to validate the findings and define the factors that regulate illness breakout.

SIRS epidemic modeling using fractional-ordered differential equations: Role of fear effect

In this paper, an SIRS epidemic model using Grunwald–Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases. The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number. The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter. Additionally, using the Grunwald–Letnikov approximation, the simulation is carried out to confirm the validity of analytic results graphically. Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021, we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one. Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases. [ FROM AUTHOR] Copyright of International Journal of Biomathematics is the property of World Scientific Publishing Company 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.)

Projection of COVID-19 Jakarta using CHIME Technology (Covid-19 Hospital Impact Model for Epidemics) Application

After the coronavirus outbreak, the disease known as COVID-19 has been infecting millions of people, and the number of deaths is pilling up to hundreds of thousands. In Indonesia, especially Jakarta, some of the deaths are caused by pandemic-related surges that strain hospital capacity. Besides, people had many obstacles in this pandemic condition because of the lack of knowledge about COVID-19. On that matter, several models emerged worldwide to help inform public decision making in this pandemic situation. With today's technological advances the CHIME (COVID-19 Hospital Impact Model for Epidemics) application is designed to assist hospitals and public health officials with understanding hospital capacity needs as they relate to the COVID pandemic. This paper aims to help inform public health decision making regarding the transmission of COVID-19 in Jakarta using CHIME. This work uses Jakarta COVID-19 data from November 24th, 2021 and its accumulation from 14 days before (November 10th, 2021) to predict the course of COVID-19 in 30 days. With ArcGIS Pro and ArcGIS Experience, this work successfully made a map that uses CHIME to inform about peak demand of each city in DKI Jakarta and the daily new admissions and hospitalization graph. In addition, a Jakarta COVID-19 dashboard is also made to inform more about the transmission of COVID-19. © 2022 IEEE.

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number (R0) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of R0 to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time -dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

Supply Chain Risk Diffusion in Partially Mapping Double-Layer Hypernetworks.

The impact of COVID-19 is global, and uncertain information will affect product quality and worker efficiency in the complex supply chain network, thus bringing risks. Aiming at individual heterogeneity, a partial mapping double-layer hypernetwork model is constructed to study the supply chain risk diffusion under uncertain information. Here, we explore the risk diffusion dynamics, drawing on epidemiology, and establish an SPIR (Susceptible-Potential-Infected-Recovered) model to simulate the risk diffusion process. The node represents the enterprise, and hyperedge represents the cooperation among enterprises. The microscopic Markov chain approach (MMCA) is used to prove the theory. Network dynamic evolution includes two removal strategies: (i) removing aging nodes; (ii) removing key nodes. Using Matlab to simulate the model, we found that it is more conducive to market stability to eliminate outdated enterprises than to control key enterprises during risk diffusion. The risk diffusion scale is related to interlayer mapping. Increasing the upper layer mapping rate to strengthen the efforts of official media to issue authoritative information will reduce the infected enterprise number. Reducing the lower layer mapping rate will reduce the misled enterprise number, thereby weakening the efficiency of risk infection. The model is helpful for understanding the risk diffusion characteristics and the importance of online information, and it has guiding significance for supply chain management.

Stability analysis of an epidemic model with vaccination and time delay

This paper presents an epidemic model with varying population, incorporating a new vaccination strategy and time delay. It investigates the impact of vaccination with respect to vaccine efficacy and the time required to see the effects, followed by determining how to control the spread of the disease according to the basic reproduction ratio of the disease. Some numerical simulations are provided to illustrate the theoretical results.

A review on epidemic models in sight of fractional calculus

Biomathematics has become one of the most significant areas of research as a result of interdisciplinary study. Chronic diseases sometimes referred to as non-communicable and communicable diseases, are conditions that develop over an extended period as a result of different factors like genetics, lifestyle, and environment. The most important common types of disease are cardiovascular, alcohol, cancer, and diabetes. More than three-quarters of the world's (31.4 million) deaths occur in low- and middle-income nations, which are disproportionately affected by different infections. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. Recently, researchers have actively considered fractional calculus to study different diseases like COVID-19, cancer, TB, HIV, dengue fever, diabetes, cholera, pine welts, smoking and heart attacks, etc. With the help of fractional operator, we modified a mathematical model for the dynamical transmission, analysis, treatment, vaccination, and precaution leveling necessary to mitigate the negative impact of illness on society in the long run, overcoming the memory effect without defining or considering others parameters. In this review paper, we considered all the recent studies based on the fractional modeling of infectious and non-infectious diseases with different fractional operators such as Caputo, Caputo Fabrizio, ABC, and constant proportional with Caputo, etc. This review paper aims to bring all the information together by considering different fractional operators and their uses in the field of infectious disease modeling. The steps taken to accomplish the goal were developing a mathematical model, identifying the equilibrium point, figuring out the minimal reproductive number, and assessing the stability around the equilibrium point. For future direction, we consider the cancer model to study the growth cells of cancer and the impact of therapy to control infections. An equilibrium solution and an analysis of the behavior dynamics of the cell spread with treatment in the form of chemotherapy were obtained. The simulation shows that the population of cancer cells is influenced by the pace of cancer cell growth with the Caputo fractional derivative. The acquired results show how effective and precise the suggested approach is in helping to better understand how chemotherapy works. Chemotherapy medications have been found to increase immunity against particular cancer by reducing the number of tumor cells. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Our innovative methodology might have significant effects on global stakeholders, policymakers, and national health systems. The current strategies for controlling outbreaks and the vaccination and prevention policies that have been implemented would benefit from a more accurate representation of the dynamics of contagious diseases, which necessitates the development of highly complex mathematical models. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples.

Wastewater-based modeling, reconstruction, and prediction for COVID-19 outbreaks in Hungary caused by highly immune evasive variants.

(MOTIVATION): Wastewater-based epidemiology (WBE) has emerged as a promising approach for monitoring the COVID-19 pandemic, since the measurement process is cost-effective and is exposed to fewer potential errors compared to other indicators like hospitalization data or the number of detected cases. Consequently, WBE was gradually becoming a key tool for epidemic surveillance and often the most reliable data source, as the intensity of clinical testing for COVID-19 drastically decreased by the third year of the pandemic. Recent results suggests that the model-based fusion of wastewater measurements with clinical data and other indicators is essential in future epidemic surveillance. (METHOD): In this work, we developed a wastewater-based compartmental epidemic model with a two-phase vaccination dynamics and immune evasion. We proposed a multi-step optimization-based data assimilation method for epidemic state reconstruction, parameter estimation, and prediction. The computations make use of the measured viral load in wastewater, the available clinical data (hospital occupancy, delivered vaccine doses, and deaths), the stringency index of the official social distancing rules, and other measures. The current state assessment and the estimation of the current transmission rate and immunity loss allow a plausible prediction of the future progression of the pandemic. (RESULTS): Qualitative and quantitative evaluations revealed that the contribution of wastewater data in our computational epidemiological framework makes predictions more reliable. Predictions suggest that at least half of the Hungarian population has lost immunity during the epidemic outbreak caused by the BA.1 and BA.2 subvariants of Omicron in the first half of 2022. We obtained a similar result for the outbreaks caused by the subvariant BA.5 in the second half of 2022. (APPLICABILITY): The proposed approach has been used to support COVID management in Hungary and could be customized for other countries as well.

Modeling The Effect of Contaminated Object, Vaccination and Treatment on The Diseases Epidemiology

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.

Advanced Nonlinear Robust Approach for Controlling COVID-19 System Based on Vaccination Campaign

This study proposes a new approach for controlling COVID-19 through vaccination, where an adequately descriptive mathematical model is created for COVID-19 using the susceptible exposed infectious recovered (SEIR) model of epidemic diseases. The presented control approach is synthesized using a combination of feedback linearization and H∞ control, and incorporates model reference control to achieve optimal time responses with the aid of the black hole optimization (BHO) algorithm. The effectiveness of the designed control law is evaluated using data from the lombardy region of Italy. The results of the simulation show that the proposed control approach is able to effectively control the COVID-19 outbreak by accurately implementing the desirable vaccination, while effectively addressing nonlinearity and uncertainty in the COVID-19 system with a desirable control action. The control method has achieved the required immunity of 6.6 million individuals after approximately 25 days with a transmission rate reduced to zero in a short time, and a vaccination rate of 170 thousand people per day © 2023, International Journal of Intelligent Engineering and Systems.All Rights Reserved.

Computational modeling of fractional COVID-19 model by Haar wavelet collocation Methods with real data.

This study explores the use of numerical simulations to model the spread of the Omicron variant of the SARS-CoV-2 virus using fractional-order COVID-19 models and Haar wavelet collocation methods. The fractional order COVID-19 model considers various factors that affect the virus's transmission, and the Haar wavelet collocation method offers a precise and efficient solution to the fractional derivatives used in the model. The simulation results yield crucial insights into the Omicron variant's spread, providing valuable information to public health policies and strategies designed to mitigate its impact. This study marks a significant advancement in comprehending the COVID-19 pandemic's dynamics and the emergence of its variants. The COVID-19 epidemic model is reworked utilizing fractional derivatives in the Caputo sense, and the model's existence and uniqueness are established by considering fixed point theory results. Sensitivity analysis is conducted on the model to identify the parameter with the highest sensitivity. For numerical treatment and simulations, we apply the Haar wavelet collocation method. Parameter estimation for the recorded COVID-19 cases in India from 13 July 2021 to 25 August 2021 has been presented.

A novel mathematical model for prioritization of individuals to receive vaccine considering governmental health protocols.

Infectious diseases drive countries to provide vaccines to individuals. Due to the limited supply of vaccines, individuals prioritize receiving vaccinations worldwide. Although, priority groups are formed based on age groupings due to the restricted decision-making time. Governments usually ordain different health protocols such as lockdown policy, mandatory use of face masks, and vaccination during the pandemics. Therefore, this study considers the case of COVID-19 with a SEQIR (susceptible-exposed-quarantined-infected-recovered) epidemic model and presents a novel prioritization technique to minimize the social and economic impacts of the lockdown policy. We use retail units as one of the affected parts to demonstrate how a vaccination plan may be more effective if individuals such as retailers were prioritized and age groups. In addition, we estimate the total required vaccine doses to control the epidemic disease and compute the number of vaccine doses supplied by various suppliers. The vaccine doses are determined using optimal control theory in the solution technique. In addition, we consider the effect of the mask using policy in the number of vaccine doses allocated to each priority group. The model's performance is evaluated using an illustrative scenario based on a real case.

Global stability analysis of a COVID-19 epidemic model with incubation delay

In this paper, we propose, analyze and simulate a time delay differential equation to investigate the transmission and spread of Coronavirus disease (COVID-19). The basic reproduction number of the model is determined and qualitatively used to investigate the global stability of the model's steady states. We use numerical simulations to support the analytical results in the study. From the simulation results, we note that whenever the basic reproduction number is greater than unity, the model solutions will be associated with periodic oscillations for a considerable time scale from the start before attaining stability. This suggests that the inclusion of the time delay factor destabilizes the endemic equilibrium point leading to periodic solutions that arise due to Hopf bifurcations for a certain time frame.

Using linear regression metamodels for evaluating interventions in an individual-based influenza epidemic model

Agent-based simulation modeling is frequently used to model and simulate the spread of transmissible diseases such as influenza, COVID-19, and HIV/AIDS in communities. Besides incorporating disease-specific parameters, these models include a set of parameters to observe the effect of different intervention combinations on the course of an epidemic, bringing the opportunity to use these models as virtual laboratories for decision-making. However, these models are primarily large-scale and complex, increasing the runtime of experimentation. As a solution, metamodeling approaches are frequently employed to represent input–output relationships of simulation models. Instead of running the time-consuming agent-based model, policymakers use the metamodel to obtain predicted outcomes in a comparatively short time. In addition to time-saving advantages, metamodels can provide insights into how disease-specific and intervention parameters affect the outcome of interest. In this regard, this study uses an influenza epidemic model, FluTE, as the experimental platform. Instead of using the original agent-based model, we fit linear regression metamodels to quantify the effect of interventions, such as vaccination, quarantine, and school closure, on the influenza attack rate. After validating the metamodel, we observe that the day on which interventions start, ascertainment delay, the daily number of vaccinations administered, isolation and quarantine compliance probabilities, and the number of school closure days stand as the significant intervention policies.

A Kermack-McKendrick model with age of infection starting from a single or multiple cohorts of infected patients

The infectiousness of infected individuals is known to depend on the time since the individual was infected, called the age of infection. Here, we study the parameter identifiability of the Kermack-McKendrick model with age of infection which takes into account this dependency. By considering a single cohort of individuals, we show that the daily reproduction number can be obtained by solving a Volterra integral equation that depends on the flow of newly infected individuals. We test the consistency of the method by generating data from deterministic and stochastic numerical simulations. Finally, we apply our method to a dataset from SARS-CoV-1 with detailed information on a single cluster of patients. We stress the necessity of taking into account the initial data in the analysis to ensure the identifiability of the problem.

Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment

The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters beta and delta, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.

Certain efficient techniques to solve the unreported cases of 2019-nCoV epidemic model

One of the furthermost intimidations that the death faced after the second World War is 2019-nCoV epidemic and most crucial large-scale health disaster of this century. We devote the current work to discuss the epidemic prediction for the epidemic model created for 2019-nCoV in Wuhan, China by certain approximate analytical methods such as differential transform method and variational iteration method. Further, we recognize unreported cases in numbers and the parameters of model are due to reported case data. For the considered system demonstrating the model of coronavirus, the series solution is conventional in the structure of the differential transform method. The obtained solutions are discussed in figures which show the performance of considered model. The results show that the used schemes are definite and trouble-free to execution for the system of nonlinear ODEs. The solutions exposed that the both schemes are in total agreement, correct and well-organized for solving systems of nonlinear differential equations.

New Trends in Fuzzy Modeling Through Numerical Techniques

Amoebiasis is a parasitic intestinal infection caused by the highly pathogenic amoeba Entamoeba histolytica. It is spread through person-to -person contact or by eating or drinking food or water contaminated with feces. Its transmission rate depends on the number of cysts present in the environment. The traditional models assumed a homogeneous and contra-dictory transmission with reality. The heterogeneity of its transmission rate is a significant factor when modeling disease dynamics. The heterogeneity of disease transmission can be described mathematically by introducing fuzzy theory. In this context, a fuzzy SEIR Amoebiasis disease model is consid-ered in this study. The equilibrium analysis and reproductive number are studied with fuzziness. Two numerical schemes forward Euler method and a nonstandard finite difference (NSFD) approach, are developed for the learned model, and the results of numerical simulations are presented. The numerical and simulation results reveal that the proposed NSFD method provides an adequate representation of the dynamics of the disease despite the uncertainty and heterogeneity. Moreover, the obtained method generates plausible predictions that regulators can use to support decision-making to design and develop control strategies.