Investigation of interactions between COVID-19 and diabetes with hereditary traits using real data: A case study in Turkey

Mathematical model for understanding the relationship between diabetes and novel coronavirus

A new model is proposed to explore interactions between diabetes and novel coronavirus. The model accounted for both the omicron variant and variants varying from omicron. The model investigated compartments such as hospitalization, diabetes, co-infection, omicron variant, and quarantine. Additionally, the impact of different vaccination doses is assessed. Sensitivity analysis is carried out to determine disease prevalence and control options, emphasizing the significance of knowing epidemics and their characteristics. The model is validated using actual data from Japan. The parameters are fitted with the help of "Least Square Curve Fitting" method to describe the dynamic behavior of the proposed model. Simulation results and theoretical findings demonstrate the dynamic behavior of novel coronavirus and diabetes mellitus (DM). Biological illustrations that illustrate impact of model parameters are evaluated. Furthermore, effect of vaccine efficacy and vaccination rates for the vaccine's first, second, and booster doses is conducted. The impact of various preventive measures, such as hospitalization rate, quarantine or self-isolation rate, vaccine dose-1, dose-2, and booster dose, is considered for diabetic individuals in contact with symptomatic or asymptomatic COVID-19 infectious people in the proposed model. The findings demonstrate the significance of vaccine doses on people with diabetes and individuals infectious with omicron variant. The proposed work helps with subsequent prevention efforts and the design of a vaccination policy to mitigate the effect of the novel coronavirus.

Analysis of age wise fractional order problems for the Covid-19 under non-singular kernel of Mittag-Leffler law

The developed article considers SIR problems for the recent COVID-19 pandemic, in which each component is divided into two subgroups: young and adults. These subgroups are distributed among two classes in each compartment, and the effect of COVID-19 is observed in each class. The fractional problem is investigated using the non-singular operator of Atangana Baleanu in the Caputo sense (ABC). The existence and uniqueness of the solution are calculated using the fundamental theorems of fixed point theory. The stability development is also determined using the Ulam-Hyers stability technique. The approximate solution is evaluated using the fractional Adams-Bashforth technique, providing a wide range of choices for selecting fractional order parameters. The simulation is plotted against available data to verify the obtained scheme. Different fractional-order approximations are compared to integer-order curves of various orders. Therefore, this analysis represents the recent COVID-19 pandemic, differentiated by age at different fractional orders. The analysis reveals the impact of COVID-19 on young and adult populations. Adults, who typically have weaker immune systems, are more susceptible to infection compared to young people. Similarly, recovery from infection is higher among young infected individuals compared to infected cases in adults.

Stability Analysis of SARS-CoV-2 with Heart Attack Effected Patients and Bifurcation

The aim of this study is to analyze and investigate the SARS-CoV-2 (SC-2) transmission with effect of heart attack in United Kingdom with advanced mathematical tools. Mathematical model is converted into fractional order with the help of fractal fractional operator (FFO). The proposed fractional order system is investigated qualitatively as well as quantitatively to identify its stable position. Local stability of the SC-2 system is verified and test the proposed system with flip bifurcation. Also system is investigated for global stability using Lyponove first and second derivative functions. The existence, boundedness, and positivity of the SC-2 is checked which are the key properties for such of type of epidemic problem to identify reliable findings. Effect of global derivative is demonstrated to verify its rate of effects of heart attack in united kingdom. Solutions for fractional order system are derived with the help of advanced tool FFO for different fractional values to verify the combine effect of COVID-19 and heart patients. Simulation are carried out to see symptomatic as well as a symptomatic effects of SC-2 in the United Kingdom as well as its global effects, also show the actual behavior of SC-2 which will be helpful to understand the outbreak of SC-2 for heart attack patients and to see its real behavior globally as well as helpful for future prediction and control strategies.

The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies

This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model's equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease's dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

Transition dynamics between a novel coinfection model of fractional-order for COVID-19 and tuberculosis via a treatment mechanism

In this paper, a fractional-order coinfection model for the transmission dynamics of COVID-19 and tuberculosis is presented. The positivity and boundedness of the proposed coinfection model are derived. The equilibria and basic reproduction number of the COVID-19 sub-model, Tuberculosis sub-model, and COVID-19 and Tuberculosis coinfection model are derived. The local and global stability of both the COVID-19 and Tuberculosis sub-models are discussed. The equilibria of the coinfection model are locally asymptotically stable under certain conditions. Later, the impact of COVID-19 on TB and TB on COVID-19 is analyzed. Finally, the numerical simulation is carried out to assess the effect of various biological parameters in the transmission dynamics of COVID-19 and Tuberculosis coinfection.

A memory effect model to predict COVID-19: analysis and simulation

On 19 September 2020, the Centers for Disease Control and Prevention (CDC) recommended that asymptomatic individuals, those who have close contact with infected person, be tested. Also, American society for biological clinical comments on testing of asymptomatic individuals. So, we proposed a new mathematical model for evaluating the population-level impact of contact rates (social-distancing) and the rate at which asymptomatic people are hospitalized (isolated) following testing due to close contact with documented infected people. The model is a deterministic system of nonlinear differential equations that is fitted and parameterized by least square curve fitting using COVID-19 pandemic data of Pakistan from 1 October 2020 to 30 April 2021. The fractional derivative is used to understand the biological process with crossover behavior and memory effect. The reproduction number and conditions for asymptotic stability are derived diligently. The most common non-integer Caputo derivative is used for deeper analysis and transmission dynamics of COVID-19 infection. The fractional-order Adams-Bashforth method is used for the solution of the model. In light of the dynamics of the COVID-19 outbreak in Pakistan, non-pharmaceutical interventions (NPIs) in terms of social distancing and isolation are being investigated. The reduction in the baseline value of contact rates and enhancement in hospitalization rate of symptomatic can lead the elimination of the pandemic.

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control

Clinical reports have shown that chronic hepatitis B virus (HBV) patients co-infected with SARS-CoV-2 have a higher risk of complications with liver disease than patients without SARS-CoV-2. In this work, a co-dynamical model is designed for SARS-CoV-2 and HBV which incorporates incident infection with the dual diseases. Existence of boundary and co-existence endemic equilibria are proved. The occurrence of backward bifurcation, in the absence and presence of incident co-infection, is investigated through the proposed model. It is noted that in the absence of incident co-infection, backward bifurcation is not observed in the model. However, incident co-infection triggers this phenomenon. For a special case of the study, the disease free and endemic equilibria are shown to be globally asymptotically stable. To contain the spread of both infections in case of an endemic situation, the time dependent controls are incorporated in the model. Also, global sensitivity analysis is carried out by using appropriate ranges of the parameter values which helps to assess their level of sensitivity with reference to the reproduction numbers and the infected components of the model. Finally, numerical assessment of the control system using various intervention strategies is performed, and reached at the conclusion that enhanced preventive efforts against incident co-infection could remarkably control the co-circulation of both SARS-CoV-2 and HBV.

On the analysis of the fractional model of COVID-19 under the piecewise global operators

An expanding field of study that offers fresh and intriguing approaches to both mathematicians and biologists is the symbolic representation of mathematics. In relation to COVID-19, such a method might provide information to humanity for halting the spread of this epidemic, which has severely impacted people's quality of life. In this study, we examine a crucial COVID-19 model under a globalized piecewise fractional derivative in the context of Caputo and Atangana Baleanu fractional operators. The said model has been constructed in the format of two fractional operators, having a non-linear time-varying spreading rate, and composed of ten compartmental individuals: Susceptible, Infectious, Diagnosed, Ailing, Recognized, Infectious Real, Threatened, Recovered Diagnosed, Healed and Extinct populations. The qualitative analysis is developed for the proposed model along with the discussion of their dynamical behaviors. The stability of the approximate solution is tested by using the Ulam-Hyers stability approach. For the implementation of the given model in the sense of an approximate piecewise solution, the Newton Polynomial approximate solution technique is applied. The graphing results are with different additional fractional orders connected to COVID-19 disease, and the graphical representation is established for other piecewise fractional orders. By using comparisons of this nature between the graphed and analytical data, we are able to calculate the best-fit parameters for any arbitrary orders with a very low error rate. Additionally, many parameters' effects on the transmission of viral infections are examined and analyzed. Such a discussion will be more informative as it demonstrates the dynamics on various piecewise intervals.

Evaluating the impact of multiple factors on the control of COVID-19 epidemic: A modelling analysis using India as a case study

The currently ongoing COVID-19 outbreak remains a global health concern. Understanding the transmission modes of COVID-19 can help develop more effective prevention and control strategies. In this study, we devise a two-strain nonlinear dynamical model with the purpose to shed light on the effect of multiple factors on the outbreak of the epidemic. Our targeted model incorporates the simultaneous transmission of the mutant strain and wild strain, environmental transmission and the implementation of vaccination, in the context of shortage of essential medical resources. By using the nonlinear least-square method, the model is validated based on the daily case data of the second COVID-19 wave in India, which has triggered a heavy load of confirmed cases. We present the formula for the effective reproduction number and give an estimate of it over the time. By conducting Latin Hyperbolic Sampling (LHS), evaluating the partial rank correlation coefficients (PRCCs) and other sensitivity analysis, we have found that increasing the transmission probability in contact with the mutant strain, the proportion of infecteds with mutant strain, the ratio of probability of the vaccinated individuals being infected, or the indirect transmission rate, all could aggravate the outbreak by raising the total number of deaths. We also found that increasing the recovery rate of those infecteds with mutant strain while decreasing their disease-induced death rate, or raising the vaccination rate, both could alleviate the outbreak by reducing the deaths. Our results demonstrate that reducing the prevalence of the mutant strain, improving the clearance of the virus in the environment, and strengthening the ability to treat infected individuals are critical to mitigate and control the spread of COVID-19, especially in the resource-constrained regions.

A fractal-fractional COVID-19 model with a negative impact of quarantine on the diabetic patients

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

It is well established that COVID-19 incidence data follows some power law growth pattern. Therefore, it is natural to believe that the COVID-19 transmission process follows some power law. However, we found no existing model on COVID-19 with a power law effect only in the disease transmission process. Inevitably, it is not clear how this power law effect in disease transmission can influence multiple COVID-19 waves in a location. In this context, we developed a completely new COVID-19 model where a force of infection function in disease transmission follows some power law. Furthermore, different realistic epidemiological scenarios like imperfect social distancing among home-quarantined individuals, disease awareness, vaccination, treatment, and possible reinfection of the recovered population are also considered in the model. Applying some recent techniques, we showed that the proposed system converted to a COVID-19 model with fractional order disease transmission, where order of the fractional derivative ( α ) in the force of infection function represents the memory effect in disease transmission. We studied some mathematical properties of this newly formulated model and determined the basic reproduction number (R 0 ). Furthermore, we estimated several epidemiological parameters of the newly developed fractional order model (including memory index α ) by fitting the model to the daily reported COVID-19 cases from Russia, South Africa, UK, and USA, respectively, for the time period March 01, 2020, till December 01, 2021. Variance-based Sobol's global sensitivity analysis technique is used to measure the effect of different important model parameters (including α ) on the number of COVID-19 waves in a location (W C ). Our findings suggest that α along with the average transmission rate of the undetected (symptomatic and asymptomatic) cases in the community (β 1 ) are mainly influencing multiple COVID-19 waves in those four locations. Numerically, we identified the regions in the parameter space of α andβ 1 for which multiple COVID-19 waves are occurring in those four locations. Furthermore, our findings suggested that increasing memory effect in disease transmission ( α → 0) may decrease the possibility of multiple COVID-19 waves and as well as reduce the severity of disease transmission in those four locations. Based on all the results, we try to identify a few non-pharmaceutical control strategies that may reduce the risk of further SARS-CoV-2 waves in Russia, South Africa, UK, and USA, respectively.

SARS-CoV-2 transmission in university classes

We investigate transmission dynamics for SARS-CoV-2 on a real network of classes at Simon Fraser University. Outbreaks are simulated over the course of one semester across numerous parameter settings, including moving classes above certain size thresholds online. Regression trees are used to analyze the effect of disease parameters on simulation outputs. We find that an aggressive class size thresholding strategy is required to mitigate the risk of a large outbreak, and that transmission by symptomatic individuals is a key driver of outbreak size. These findings provide guidance for designing control strategies at other institutions, as well as setting priorities and allocating resources for disease monitoring.

Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

In this paper, we explore local behavior at fixed points, chaos and bifurcations of a discrete COVID-19 epidemic model in the interior of R + 5 . It is explored that for all involved parametric values, COVID-19 model has boundary fixed point and also it has an interior fixed point under certain parametric condition(s). We have investigated local behavior at boundary and interior fixed points of COVID-19 model by linear stability theory. It is also explored the existence of possible bifurcations at respective fixed points, and proved that at boundary fixed point there exists no flip bifurcation but at interior fixed point it undergoes both flip and hopf bifurcations, and we have explored said bifurcations by explicit criterion. Moreover, chaos in COVID-19 model is also investigated by feedback control strategy. Finally, theoretical results are verified numerically.

A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function☆

The aim of this paper is to present and analyze the fractional optimal control model for COVID-19 and diabetes co-dynamics, using the Atangana-Baleanu derivative. The positivity and boundedness of the solutions was shown by the method of Laplace transform. The existence and uniqueness of the solutions of the proposed model were established using Banach fixed point Theorem and Leray–Schauder alternative Theorem. The fractional model was also shown to be Hyers-Ulam stable. The model was fitted to the cumulative confirmed daily COVID-19 cases for Indonesia. The simulations of the total number of hospitalized individuals co-infected with COVID-19 and diabetes, at different face-mask compliance levels, when vaccination strategy is maintained reveals that the total number of hospitalized co-infection cases decreases with increase in face-mask compliance levels, while maintaining COVID-19 vaccination. The simulation results show that to curtail COVID-19 and diabetes co-infections, policies and measures to enforce mass COVID-19 vaccination and strict face-mask usage in the public must be put in place. To further cut down the spread of COVID-19 and diabetes co-infection, time dependent controls are added into the fractional model, and the obtained optimal control problem investigated via the Pontryagin’s Maximum Principle.

Mathematical modeling of corona virus (COVID-19) and stability analysis

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us.

Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling

The fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.

Analysis of mobility based COVID-19 epidemic model using Federated Multitask Learning

Aggregating a massive amount of disease-related data from heterogeneous devices, a distributed learning framework called Federated Learning(FL) is employed. But, FL suffers in distributing the global model, due to the heterogeneity of local data distributions. To overcome this issue, personalized models can be learned by using Federated multitask learning(FMTL). Due to the heterogeneous data from distributed environment, we propose a personalized model learned by federated multitask learning (FMTL) to predict the updated infection rate of COVID-19 in the USA using a mobility-based SEIR model. Furthermore, using a mobility-based SEIR model with an additional constraint we can analyze the availability of beds. We have used the real-time mobility data sets in various states of the USA during the years 2020 and 2021. We have chosen five states for the study and we observe that there exists a correlation among the number of COVID-19 infected cases even though the rate of spread in each case is different. We have considered each US state as a node in the federated learning environment and a linear regression model is built at each node. Our experimental results show that the root-mean-square percentage error for the actual and prediction of COVID-19 cases is low for Colorado state and high for Minnesota state. Using a mobility-based SEIR simulation model, we conclude that it will take at least 400 days to reach extinction when there is no proper vaccination or social distance.

Stationary distribution and extinction of a stochastic influenza virus model with disease resistance

Influenza is a respiratory infection caused influenza virus. To evaluate the effect of environment noise on the transmission of influenza, our study focuses on a stochastic influenza virus model with disease resistance. We first prove the existence and uniqueness of the global solution to the model. Then we obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Moreover, certain sufficient conditions are provided for the extinction of the influenza virus flu. Finally, several numerical simulations are revealed to illustrate our theoretical results. Conclusively, according to the results of numerical models, increasing disease resistance is favorable to disease control. Furthermore, a simple example demonstrates that white noise is favorable to the disease's extinction.

A fractional order model for the co-interaction of COVID-19 and Hepatitis B virus

Fractional differential equations are beginning to gain widespread usage in modeling physical and biological processes. It is worth mentioning that the standard mathematical models of integer-order derivatives, including nonlinear models, do not constitute suitable framework in many cases. In this work, a mathematical model for COVID-19 and Hepatitis B Virus (HBV) co-interaction is developed and studied using the Atangana-Baleanu fractional derivative. The necessary conditions of the existence and uniqueness of the solution of the proposed model are studied. The local stability analysis is carried out when the reproduction number is less than one. Using well constructed Lyapunov functions, the disease free and endemic equilibria are proven to be globally asymptotically stable under certain conditions. Employing fixed point theory, the stability of the iterative scheme to approximate the solution of the model is discussed. The model is fitted to real data from the city of Wuhan, China, and important parameters relating to each disease and their co-infection, are estimated from the fitting. The approximate solutions of the model are compared using the integer and fractional order derivatives. The impact of the fractional derivative on the proposed model is also highlighted. The results proven in this paper illustrate that HBV and COVID-19 transmission rates can greatly impact the dynamics of the co-infection of both diseases. It is concluded that to control the co-circulation of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

In co-infection models for two diseases, it is mostly claimed that, the dynamical behavior of the sub-models usually predict or drive the behavior of the complete models. However, under a certain assumption such as, allowing incident co-infection with both diseases, we have a different observation. In this paper, a new mathematical model for SARS-CoV-2 and Zika co-dynamics is presented which incorporates incident co-infection by susceptible individuals. It is worth mentioning that the assumption is missing in many existing co-infection models. We shall discuss the impact of this assumption on the dynamics of a co-infection model. The model also captures sexual transmission of Zika virus. The positivity and boundedness of solution of the proposed model are studied, in addition to the local asymptotic stability analysis. The model is shown to exhibit backward bifurcation caused by the disease-induced death rates and parameters associated with susceptibility to a second infection by those singly infected. Using Lyapunov functions, the disease free and endemic equilibria are shown to be globally asymptotically stable for R 0 1 , respectively. To manage the co-circulation of both infections effectively, under an endemic setting, time dependent controls in the form of SARS-CoV-2, Zika and co-infection prevention strategies are incorporated into the model. The simulations show that SARS-CoV-2 prevention could greatly reduce the burden of co-infections with Zika. Furthermore, it is also shown that prevention controls for Zika can significantly decrease the burden of co-infections with SARS-CoV-2.

Out-of-Season Influenza during a COVID-19 Void in the State of Rio de Janeiro, Brazil: Temperature Matters

An out-of-season H3N2 type A influenza epidemic occurred in the State of Rio de Janeiro, Brazil during October-November 2021, in between the Delta and Omicron SARS-CoV-2 surges, which occurred in July-October 2021 and January-April 2022, respectively. We assessed the contribution of climate change and influenza immunization coverage in this unique, little publicized phenomenon. State weather patterns during the influenza epidemic were significantly different from the five preceding years, matching typical winter temperatures, associated with the out-of-season influenza. We also found a mismatch between influenza vaccine strains used in the winter of 2021 (trivalent vaccine with two type A strains (Victoria/2570/2019 H1N1, Hong Kong/2671/2019 H3N2) and one type B strain (Washington/02/2019, wild type) and the circulating influenza strain responsible for the epidemic (H3N2 Darwin type A influenza strain). In addition, in 2021, there was poor influenza vaccine coverage with only 56% of the population over 6 months old immunized. Amid the COVID-19 pandemic, we should be prepared for out-of-season outbreaks of other respiratory viruses in periods of COVID-19 remission, which underscore novel disease dynamics in the pandemic era. The availability of year-round influenza vaccines could help avoid unnecessary morbidity and mortality given that antibodies rapidly wane. Moreover, this would enable unimmunized individuals to have additional opportunities to vaccinate during out-of-season outbreaks.

Predicting the spread of COVID-19 with a machine learning technique and multiplicative calculus

This paper aims to generate a universal well-fitted mathematical model to aid global representation of the spread of the coronavirus (COVID-19) disease. The model aims to identify the importance of the measures to be taken in order to stop the spread of the virus. It describes the diffusion of the virus in normal life with and without precaution. It is a data-driven parametric dependent function, for which the parameters are extracted from the data and the exponential function derived using multiplicative calculus. The results of the proposed model are compared to real recorded data from different countries and the performance of this model is investigated using error analysis theory. We stress that all statistics, collected data, etc., included in this study were extracted from official website of the World Health Organization (WHO). Therefore, the obtained results demonstrate its applicability and efficiency.

Fractional order modelling of omicron SARS-CoV-2 variant containing heart attack effect using real data from the United Kingdom

In this study, a new approach to COVID-19 pandemic is presented. In this context, a fractional order pandemic model is developed to examine the spread of COVID-19 with and without Omicron variant and its relationship with heart attack using real data from the United Kingdom. In the model, heart attack is adopted by considering its relationship with the quarantine strategy. Then, the existence, uniqueness, positivity and boundedness of the solution are studied. The equilibrium points and their stability conditions are achieved. Subsequently, we calculate the basic reproduction number (the virus transmission coefficient) that simply refers to the number of people, to whom an infected person can make infected, asR 0 = 3.6456 by using the next generation matrix method. Next, we consider the sensitivity analysis of the parameters according to R 0 . In order to determine the values of the parameters in the model, the least squares curve fitting method, which is one of the leading methods in parameter estimation, is benefited. A total of 21 parameter values in the model are estimated by using real Omicron data from the United Kingdom. Moreover, in order to highlight the advantages of using fractional differential equations, applications related to memory trace and hereditary properties are given. Finally, the numerical simulations are presented to examine the dynamic behavior of the system. As a result of numerical simulations, an increase in the number of people who have heart attacks is observed when Omicron cases were first seen. In the future, it is estimated that the risk of heart attack will decrease as the cases of Omicron decrease.

Age Dependent Epidemic Modeling of COVID-19 Outbreak in Kuwait, France, and Cameroon

Revisiting the classical model by Ross and Kermack-McKendrick, the Susceptible−Infectious−Recovered (SIR) model used to formalize the COVID-19 epidemic, requires improvements which will be the subject of this article. The heterogeneity in the age of the populations concerned leads to considering models in age groups with specific susceptibilities, which makes the prediction problem more difficult. Basically, there are three age groups of interest which are, respectively, 0−19 years, 20−64 years, and >64 years, but in this article, we only consider two (20−64 years and >64 years) age groups because the group 0−19 years is widely seen as being less infected by the virus since this age group had a low infection rate throughout the pandemic era of this study, especially the countries under consideration. In this article, we proposed a new mathematical age-dependent (Susceptible−Infectious−Goneanewsusceptible−Recovered (SIGR)) model for the COVID-19 outbreak and performed some mathematical analyses by showing the positivity, boundedness, stability, existence, and uniqueness of the solution. We performed numerical simulations of the model with parameters from Kuwait, France, and Cameroon. We discuss the role of these different parameters used in the model; namely, vaccination on the epidemic dynamics. We open a new perspective of improving an age-dependent model and its application to observed data and parameters.

New Type Modelling of the Circumscribed Self-Excited Spherical Attractor

The fractal–fractional derivative with the Mittag–Leffler kernel is employed to design the fractional-order model of the new circumscribed self-excited spherical attractor, which is not investigated yet by fractional operators. Moreover, the theorems of Schauder’s fixed point and Banach fixed existence theory are used to guarantee that there are solutions to the model. Approximate solutions to the problem are presented by an effective method. To prove the efficiency of the given technique, different values of fractal and fractional orders as well as initial conditions are selected. Figures of the approximate solutions are provided for each case in different dimensions.

Threshold dynamics of a stochastic SIHR epidemic model of COVID-19 with general population-size dependent contact rate

In this paper, we propose a stochastic SIHR epidemic model of COVID-19. A basic reproduction number $ R_{0}^{s} $ is defined to determine the extinction or persistence of the disease. If $ R_{0}^{s} < 1 $, the disease will be extinct. If $ R_{0}^{s} > 1 $, the disease will be strongly stochastically permanent. Based on realistic parameters of COVID-19, we numerically analyze the effect of key parameters such as transmission rate, confirmation rate and noise intensity on the dynamics of disease transmission and obtain sensitivity indices of some parameters on $ R_{0}^{s} $ by sensitivity analysis. It is found that: 1) The threshold level of deterministic model is overestimated in case of neglecting the effect of environmental noise; 2) The decrease of transmission rate and the increase of confirmed rate are beneficial to control the spread of COVID-19. Moreover, our sensitivity analysis indicates that the parameters $ \beta $, $ \sigma $ and $ \delta $ have significantly effects on $ R_0^s $.

Generalized Mittag-Leffler Kernel Form Solutions of Free Convection Heat and Mass Transfer Flow of Maxwell Fluid with Newtonian Heating: Prabhakar Fractional Derivative Approach

In this article, the effects of Newtonian heating along with wall slip condition on temperature is critically examined on unsteady magnetohydrodynamic (MHD) flows of Prabhakar-like non integer Maxwell fluid near an infinitely vertical plate under constant concentration. For the sake of generalized memory effects, a new mathematical fractional model is formulated based on a newly introduced Prabhakar fractional operator with generalized Fourier’s law and Fick’s law. This fractional model has been solved analytically and exact solutions for dimensionless velocity, concentration, and energy equations are calculated in terms of Mittag-Leffler functions by employing the Laplace transformation method. Physical impacts of different parameters such as α, Pr, β, Sc, Gr, γ, and Gm are studied and demonstrated graphically by Mathcad software. Furthermore, to validate our current results, some limiting models such as classical Maxwell model, classical Newtonian model, and fractional Newtonian model are recovered from Prabhakar fractional Maxwell fluid. Moreover, we compare the results between Maxwell and Newtonian fluids for both fractional and classical cases with and without slip conditions, showing that the movement of the Maxwell fluid is faster than viscous fluid. Additionally, it is visualized that both classical Maxwell and viscous fluid have relatively higher velocity as compared to fractional Maxwell and viscous fluid.

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR. For proving the existence of a unique solution, we use some recent novel properties of Mittag–Leffler function along with the fixed point theory. The stability of the proposed system is also proved by using Ulam–Hyers technique. For deriving the fractional-order numerical solution, we use the well-known Adams–Bashforth–Moulton scheme along with its stability. Graphs are plotted to understand the given chemical reaction practically. The main reason to use the Caputo-type fractional model for solving the ASR system is to propose a novel mathematical formulation through which the ASR mechanism can be efficiently explored. This paper clearly shows the importance of fractional derivatives in the study of chemical reactions.