Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel

Study of fractional order rabies transmission model via Atangana-Baleanu derivative

In this work, we aim at disentangling the theoretical contribution through mathematical modeling approach to advance the understanding of rabies dynamics and control in livestock population. A fractional order model of rabies, using Atangana-Baleanu fractional operator is created. The analysis of suggested system and its application are both conducted. The capacity of proposed model to forecast the disease can help researchers and livestock health care agencies to take preventive actions.

The transmission dynamics of an infectious disease model in fractional derivative with vaccination under real data

The resurgence of monkeypox causes considerable healthcare risks needing efficient immunization programs. This work investigates the monkeypox disease dynamics in the UK, focusing on the impact of vaccination under real data. The key difficulty is to correctly predict the spread of the disease and evaluate the success of immunization efforts. We construct a mathematical model for monkeypox infection and extend it to the fractional case considering the Caputo derivative. The analysis ensures the positivity, boundedness, and uniqueness of the solution for the non-integer system. We conduct a local asymptotical stability analysis (LAS) at the disease-free equilibrium (DFE) D0, showing the result for R0<1. Additionally, we demonstrate the existence of multiple endemic equilibria and provide conditions for backward bifurcation, which are illustrated graphically. Using real case data from the UK, we estimate model parameters via the nonlinear least square method. Our results show that, without vaccination, R2≈0.8, whereas vaccination reduces it to R2v=0.48. We perform sensitivity analysis to identify key parameters influencing disease elimination, presenting the outcomes through graphs. To solve numerically the fractional model, we outline a numerical scheme and provide detailed results under various parameter assumptions. Our findings suggest that high vaccine efficacy, a low waning rate of the vaccines, and increased vaccination of the infected people can significantly reduce the future cases of monkeypox in the UK. The present study offers a comprehensive framework for monkeypox dynamics and informs public health strategies for effective disease control and prevention.

Modelling the spatial spread of COVID-19 in a German district using a diffusion model

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion dynamics on smaller scales using partial differential equation (PDE) models. Previous works have already presented various methods to model the spatial spread of diseases, but, due to a lack of data on regional or even local scale, few actually applied their models on real disease courses in order to describe the behaviour of the disease or estimate parameters. We use medical data from both the Robert-Koch-Institute (RKI) and the Birkenfeld district government for parameter estimation within a single German district, Birkenfeld in Rhineland-Palatinate, during the second wave of the pandemic in autumn 2020 and winter 2020-21. This district can be seen as a typical middle-European region, characterized by its (mainly) rural nature and daily commuter movements towards metropolitan areas. A basic reaction-diffusion model used for spatial COVID spread, which includes compartments for susceptibles, exposed, infected, recovered, and the total population, is used to describe the spatio-temporal spread of infections. The transmission rate, recovery rate, initial infected values, detection rate, and diffusivity rate are considered as parameters to be estimated using the reported daily data and least square fit. This work also features an emphasis on numerical methods which will be used to describe the diffusion on arbitrary two-dimensional domains. Two numerical optimization techniques for parameter fitting are used: the Metropolis algorithm and the adjoint method. Two different methods, the Crank-Nicholson method and a finite element method, which are used according to the requirements of the respective optimization method are used to solve the PDE system. This way, the two methods are compared and validated and provide similar results with good approximation of the infected in both the district and the respective sub-districts.

The impact of COVID-19 on a Malaria dominated region: A mathematical analysis and simulations

One of society’s major concerns that have continued for a long time is infectious diseases. It has been demonstrated that certain disease infections, in particular multiple disease infections, make it more challenging to identify and treat infected individuals, thus deteriorating human health. As a result, a COVID-19-malaria co-infection model is developed and analyzed to study the effects of threshold quantities and co-infection transmission rate on the two diseases’ synergistic relationship. This allowed us to better understand the co-dynamics of the two diseases in the population. The existence and stability of the disease-free equilibrium of each single infection were first investigated by using their respective reproduction number. The COVID-19 and malaria-free equilibrium are locally asymptotically stable when the individual threshold quantities RC and RM are below unity. Additionally, the occurrence of the malaria prevalent equilibrium is examined, and the requirements for the backward bifurcation’s existence are provided. Sensitivity analysis reveals that the two main parameters that influence the spread of COVID-19 infection are the disease transmission rate (βc) and the fraction of the exposed individuals becoming symptomatic (ψ), while malaria transmission is influenced by the abundance of vector population, which is driven by recruitment rate (πv) with an increase in the effective biting rate (b), probability of malaria transmission per mosquito bite (βm), and probability of malaria transmission from infected humans to vectors (βv). The findings from the numerical simulation of the model show that COVID-19 will predominate in the populace and drives malaria to extinction when RM<1<RC, whereas malaria will dominate in the population and drives COVID-19 into extinction when RC<1<RM. At the disease’s endemic equilibrium, the two diseases will coexist with the one with the highest reproduction number predominating but not eradicating the other. It was demonstrated in particular that COVID-19 will invade a population where malaria is endemic if the invasion reproduction number exceeds unity. The findings also demonstrate that when the two diseases are at endemic equilibrium, the prevalence of co-infection increases COVID-19’s burden on the population while decreasing malaria incidence.

Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator

Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. There is no known vaccination or medicine until our time because the unknown aspects of the virus are more significant than our theoretical and experimental knowledge. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the disease's possibility and severity. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the disease's progress. In this study, we propose using a fractional-order SEIARPQ model with the Caputo sense to model the coronavirus (COVID-19) pandemic, which has never been done before in the literature. The stability analysis, existence, uniqueness theorems, and numerical solutions of such a model are displayed. All results were numerically simulated using MATLAB programming. The current study supports the applicability and influence of fractional operators on real-world problems.

Modeling and analysis on the transmission of covid-19 Pandemic in Ethiopia

The newest infection is a novel coronavirus named COVID-19, that initially appeared in December 2019, in Wuhan, China, and is still challenging to control. The main focus of this paper is to investigate a novel fractional-order mathematical model that explains the behavior of COVID-19 in Ethiopia. Within the proposed model, the entire population is divided into nine groups, each with its own set of parameters and initial values. A nonlinear system of fractional differential equations for the model is represented using Caputo fractional derivative. Legendre spectral collocation method is used to convert this system into an algebraic system of equations. An inexact Newton iterative method is used to solve the model system. The effective reproduction number (R0) is computed by the next-generation matrix approach. Positivity and boundedness, as well as the existence and uniqueness of solution, are all investigated. Both endemic and disease-free equilibrium points, as well as their stability, are carefully studied. We calculated the parameters and starting conditions (ICs) provided for our model using data from the Ethiopian Public Health Institute (EPHI) and the Ethiopian Ministry of Health from 22 June 2020 to 28 February 2021. The model parameters are determined using least squares curve fitting and MATLAB R2020a is used to run numerical results. The basic reproduction number is R0=1.4575. For this value, disease free equilibrium point is asymptotically unstable and endemic equilibrium point is asymptotically stable, both locally and globally.

Fractional Order Modeling the Gemini Virus in Capsicum annuum with Optimal Control

In this article, a fractional model of the Capsicum annuum (C. annuum) affected by the yellow virus through whiteflies (Bemisia tabaci) is examined. We analyzed the model by equilibrium points, reproductive number, and local and global stability. The optimal control methods are discussed to decrease the infectious B. tabaci and C. annuum by applying the Verticillium lecanii (V. lecanii) with the Atangana–Baleanu derivative. Numerical results described the population of plants and comparison values of using V. lecanni. The results show that using 60% of V. lecanni will control the spread of the yellow virus in infected B. tabaci and C. annuum in 10 days, which helps farmers to afford the costs of cultivating chili plants.

Clustering of COVID-19 data for knowledge discovery using c-means and fuzzy c-means

In this work, the partitioning clustering of COVID-19 data using c-Means (cM) and Fuzy c-Means (Fc-M) algorithms is carried out. Based on the data available from January 2020 with respect to location, i.e., longitude and latitude of the globe, the confirmed daily cases, recoveries, and deaths are clustered. In the analysis, the maximum cluster size is treated as a variable and is varied from 5 to 50 in both algorithms to find out an optimum number. The performance and validity indices of the clusters formed are analyzed to assess the quality of clusters. The validity indices to understand all the COVID-19 clusters' quality are analysed based on the Zahid SC (Separation Compaction) index, Xie-Beni Index, Fukuyama-Sugeno Index, Validity function, PC (performance coefficient), and CE (entropy) indexes. The analysis results pointed out that five clusters were identified as a major centroid where the pandemic looks concentrated. Additionally, the observations revealed that mainly the pandemic is distributed easily at any global location, and there are several centroids of COVID-19, which primarily act as epicentres. However, the three main COVID-19 clusters identified are 1) cases with value <50,000, 2) cases with a value between 0.1 million to 2 million, and 3) cases above 2 million. These centroids are located in the US, Brazil, and India, where the rest of the small clusters of the pandemic look oriented. Furthermore, the Fc-M technique seems to provide a much better cluster than the c-M algorithm.

Analysis of a COVID-19 compartmental model: a mathematical and computational approach

In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID-19. By using the free and open-source programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.

Fractional Model and Numerical Algorithms for Predicting COVID-19 with Isolation and Quarantine Strategies

In December 2019, a new outbreak in Wuhan, China has attracted world-wide attention, the virus then spread rapidly in most countries of the world, the objective of this paper is to investigate the mathematical modelling and dynamics of a novel coronavirus (COVID-19) with Caputo-Fabrizio fractional derivative in the presence of quarantine and isolation strategies. The existence and uniqueness of the solutions for the fractional model is proved using fixed point iterations, the fractional model are shown to have disease-free and an endemic equilibrium point.We construct a fractional version of the four-steps Adams-Bashforth method as well as the error estimate of this method. We have used this method to determine the numerical scheme of this model and Matlab program to illustrate the evolution of the virus in some countries (Morocco, Qatar, Brazil and Mexico) as well as to support theoretical results. The Least squares fitting is a way to find the best fit curve or line for a set of points, so we apply this method in this paper to construct an algorithm to estimate the parameters of fractional model as well as the fractional order, this model gives an estimate better than that of classical model.

Existence and data dependence results for fractional differential equations involving atangana-baleanu derivative

In the current paper, we consider multi-derivative nonlinear fractional differential equations involving Atangana-Baleanu fractional derivative. We investigate the fundamental results about the existence, uniqueness, boundedness and dependence of the solution on various data. The analysis is based on a fractional integral operator due to T. R. Prabhakar involving generalized Mittag-Leffler function, the Krasnoselskii's fixed point theorem and Gronwall-Bellman inequality with continuous functions.

Prediction studies of the epidemic peak of coronavirus disease in Brazil via new generalised Caputo type fractional derivatives

The first reported case of coronavirus disease (COVID-19) in Brazil was confirmed on 25 February 2020 and then the number of symptomatic cases produced day by day. In this manuscript, we studied the epidemic peaks of the novel coronavirus (COVID-19) in Brazil by the successful application of Predictor–Corrector (P-C) scheme. For the proposed model of COVID-19, the numerical solutions are performed by a model framework of the recent generalized Caputo type non-classical derivative. Existence of unique solution of the given non-linear problem is presented in terms of theorems. A new analysis of epidemic peaks in Brazil with the help of parameter values cited from a real data is effectuated. Graphical simulations show the obtained results to classify the importance of the classes of projected model. We observed that the proposed fractional technique is smoothly work in the coding and very easy to implement for the model of non-linear equations. By this study we tried to exemplify the roll of newly proposed fractional derivatives in mathematical epidemiology. The main purpose of this paper is to predict the epidemic peak of COVID-19 in Brazil at different transmission rates. We have also attempted to give the stability analysis of the proposed numerical technique by the reminder of some important lemmas. At last we concluded that when the infection rate increases then the nature of the diseases changes by becoming more deathly to the population.

A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model

This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Our results show similar behavior as the classical order ones. This characteristic shows the applicability and usefulness of the derivative and our numerical scheme.