The coexistence of coherent and incoherent domains in discrete coupled oscillators, chimera state, has been attracted the attention of the scientific community. Here we investigate the macroscopic dynamics of the continuous counterpart of this phenomenon. Based on a prototype model of pattern formation, we study a family of localized states. These localized solutions can be characterized by their sizes

In this work, a three-dimensional cancer model which includes the interactions between tumor cells, healthy tissue cells, and activated immune system cells was considered via Liouville–Caputo, Caputo–Fabrizio, Atangana–Baleanu, and fractional conformable derivative. We show a numerical method based on two-step Lagrange polynomial interpolation to achieve numerical approximations to these derivatives

The world is suffering from an existential global health crisis known as the COVID-19 pandemic. Countries like India, Bangladesh, and other developing countries are still having a slow pace in the detection of COVID-19 cases. Therefore, there is an urgent need for fast detection with clear visualization of infection is required using which a suspected patient of COVID-19 could be saved. Therefore,

Ever since the outbreak of novel coronavirus in December 2019, lockdown has been identified as the only effective measure across the world to stop the community spread of this pandemic. India implemented a complete shutdown across the nation from March 25, 2020 as lockdown I and went on to extend it by giving timely partial relaxations in the form of lockdown II, III & IV. This paper statistically

We report new organized structures in bi-parameter space for a nonlinear discrete predator-prey model with hunting cooperation. The intrinsic hunting cooperation among predator populations alters the dynamical behaviors of the model significantly. Especially, the stable periodic organized structures, viz. the Arnold tongues and shrimp-shaped structures in quasi-periodic and chaotic regimes exist near

Fuzzy logic via Fractal geometry is a novel mathematical combination. Using Conversion Based Fuzzy Fractal Geometry (cbFFG), researchers can approach to fractal geometry with the utilization of Direct Fuzzy Sets DFS and Fuzzy Inference Systems FIS1 in their immense fields of studies. It is proposed a new fuzzy fractal dimension FFD using membership functions instead of conventional log-log linear regression

In the high-risk modern financial market, option is an effective tool to hedge the risks caused by uncertain demand, the fluctuation of price and foreign exchange rate, because the option can provide the holder with an entitlement to sell or purchase an asset with an exercise price. The acquisition of this entitlement requires the investor to pay option fee, which raises the option pricing issue. This

In this paper, a diffusive predator-prey model subject to the zero flux boundary conditions is considered, in which the prey population exhibits social behavior and the harvesting functional of the predator population is assumed to be considered in a quadratic form. The existence of a positive solution and its bounders is investigated. The global stability of the semi trivial constant equilibrium state

The excess weight population is growing riskily in Spain. This is confirmed by the Spanish National Health Survey 2017, which gathers the percentage of overweight and obese adults in Spain from 1987 to 2017. In this paper we propose a mathematical model based on differential equations to calibrate the incidence of excess weight in the Spanish adulthood population. The main principle is that fatness

This paper addresses the soliton solutions of the Mel’nikov system by the complex amplitude ansatz method and the He’s variational principle. The bright, anti-bright, dark, anti-dark, kink, anti-kink, bell-shaped, breather and homoclinic orbits are obtained as different possible solutions of the Mel’nikov system by the two methods. The solutions and their dynamical behaviour captured by the two methods

The present article deals with certain new and interesting features of fractional blood alcohol model associated with powerful Hilfer fractional operator. The solution of the model depends on three parameters such as (i) the initial concentration of alcohol in stomach after ingestion (ii) the rate of alcohol absorption into the blood stream (ii) the rate at which the alcohol is metabolized by the liver

This article investigates a family of approximate solutions for the fractional model (in the Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev spectral collocation method). We reduce the proposed epidemiological model to a system of algebraic equations with the help of the properties of the Chebyshev polynomials of the third kind. Some theorems about the convergence

In this article we study the temporal evolution of the pandemic Sars-Cov-2 in Italy by means of dynamic population models. The time window of the available population data is between February 24, and March 25. After we upgrade the data until April 1. We perform the analysis with 4 different models and we think that the best candidate to correctly described the italian situation is a generalized Logistic

Differential operators based on convolution definitions have been recognized as powerful mathematics tools to help model real world problems due to the properties associated to their different kernels. In particular the power law kernel helps include into mathematical formulation the effect of long range, while the exponential decay helps with fading memory, also with Poisson distribution properties

The effective reproduction number (R) which signifies the number of secondary cases infected by one infectious individual, is an important measure of the spread of an infectious disease. Due to the dynamics of COVID-19 where many infected people are not showing symptoms or showing mild symptoms, and where different countries are employing different testing strategies, it is quite difficult to calculate

COVID-19 pandemic has challenged the world science. The international community tries to find, apply, or design novel methods for diagnosis and treatment of COVID-19 patients as soon as possible. Currently, a reliable method for the diagnosis of infected patients is a reverse transcription-polymerase chain reaction. The method is expensive and time-consuming. Therefore, designing novel methods is important

Italy has been one of the countries hardest hit by the coronavirus disease (COVID-19) pandemic. While the overall policy in response to the epidemic was to a large degree centralised, the regional basis of the healthcare system represented an important factor affecting the natural dynamics of the disease induced geographic specificities. Here, we characterise the region-specific modulation of COVID

In this paper, we present a novel fractional order COVID-19 mathematical model by involving fractional order with specific parameters. The new fractional model is based on the well-known Atangana–Baleanu fractional derivative with non-singular kernel. The proposed system is developed using eight fractional-order nonlinear differential equations. The Daubechies framelet system of the model is used to

A simplified model of Covid-19 epidemic dynamics under quarantine conditions and method to estimate quarantine effectiveness are developed. The model is based on the daily growth rate of new infections when total number of infections is significantly smaller than population size of infected country or region. The model is developed on the basis of collected epidemiological data of Covid19 pandemic

The rapid spread of novel coronavirus (namely Covid-19) worldwide has alarmed a pandemic since its outbreak in the city of Wuhan, China in December 2019. While the world still tries to wrap its head around as to how to contain the rapid spread of the novel coronavirus, the pandemic has already claimed several thousand lives throughout the world. Yet, the diagnosis of virus spread in humans has proven

Originating from Wuhan, China, in late 2019, and with a gradual spread in the last few months, COVID-19 has become a pandemic crossing 9 million confirmed positive cases and 450 thousand deaths. India is not only an overpopulated country but has a high population density as well, and at present, a high-risk nation where COVID-19 infection can go out of control. In this paper, we employ a compartmental

One of the common misconceptions about COVID-19 disease is to assume that we will not see a recurrence after the first wave of the disease has subsided. This completely wrong perception causes people to disregard the necessary protocols and engage in some misbehavior, such as routine socializing or holiday travel. These conditions will put double pressure on the medical staff and endanger the lives

COVID-19 emerged in Wuhan, China in December 2019 has now spread around the world causes damage to human life and economy. Pakistan is also severely effected by COVID-19 with 202,955 confirmed cases and total deaths of 4,118. Vector Autoregressive time series models was used to forecast new daily confirmed cases, deaths and recover cases for ten days. Our forecasted model results show maximum of 5

The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown epidemiological life cycle, predictive mathematical models can aid in understanding of both coronavirus disease control and management. In this study, we propose

We studied the effects of using fractional order proportional, integral, and derivative (PID) controllers in a closed-loop mathematical model of deep brain stimulation. The objective of the controller was to dampen oscillations from a neural network model of Parkinson's disease. We varied intrinsic parameters, such as the gain of the controller, and extrinsic variables, such as the excitability of

In this paper, we study Riemann Liouville fractional integral of hidden variable fractal interpolation function (HVFIF) constructed by functions whose Lipschitz exponents are in (0, 1]. Firstly, we present a construction of HVFIF using functions of which Lipschitz exponents are in (0, 1], so that the Riemann Liouville fractional integral of the HVFIF becomes a fractal interpolation function, and give

The COVID-19 pneumonia is a global threat since it emerged in early December 2019. Driven by the desire to develop a computer-aided system for the rapid diagnosis of COVID-19 to assist radiologists and clinicians to combat with this pandemic, we retrospectively collected 206 patients with positive reverse-transcription polymerase chain reaction (RT-PCR) for COVID-19 and their 416 chest computed tomography

Precipitation predictions during the flood season are critical and imperative on continents, especially in monsoon-impacted areas. However, majority of current dynamical models failed to predict the flood-season rainfall very well, although their simulations are high correct. In this study, based on the EOF decomposition of multi-factors field, we used a similar-error correction method to improve model

The novel coronavirus disease 2019 (COVID-19) began as an outbreak from epicentre Wuhan, People’s Republic of China in late December 2019, and till June 27, 2020 it caused 9,904,906 infections and 496,866 deaths worldwide. The world health organization (WHO) already declared this disease a pandemic. Researchers from various domains are putting their efforts to curb the spread of coronavirus via means

This paper performs analytical investigations on symmetric jump phenomena reflecting multi-timescale dynamics in a nonlinear shape memory alloy oscillator with parametric and external cosinoidal excitations by means of geometrical singular perturbation theory (GSPT). The conditions concerning the existence of homoclinic and heteroclinic chaos subjected to periodic perturbations are studied in mathematical

Every compactum K⊂C^ has a core decomposition DKPC with Peano quotient, which is the finest one among all upper semi-continuous decompositions into sub-continua such that the quotient space is a Peano compactum [14]. The properties of core decomposition can provide information about the topology of K. Each member of DKPC is called an atom of K. In this paper, it is shown that if {x} is an atom of a

Coronaviruses are a huge family of viruses that affect neurological, gastrointestinal, hepatic and respiratory systems. The numbers of confirmed cases are increased daily in different countries, especially in Unites State America, Spain, Italy, Germany, China, Iran, South Korea and others. The spread of the COVID-19 has many dangers and needs strict special plans and policies. Therefore, to consider

The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility. Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics. Vaccine adoption is directly affected by individual vaccination decisions, and has a complex interplay with the spatial spread of disease shaped by an underlying

Conformity has been found to play a significant role in promoting cooperation. In this paper, we propose a spatial prisoner’s dilemma game with a novel strategy updating rule, combining the payoff-driven and conformity-driven update rules. For the noise strengths κ1=κ2=0.1, our results reveal that the dynamics of this model is always absorbed into the frozen state. Three phases are appeared in the

Coronavirus genomic infection-2019 (COVID-19) has been announced as a serious health emergency arising international awareness due to its spread to 201 countries at present. In the month of April of the year 2020, it has certainly taken the pandemic outbreak of approximately 11,16,643 infections confirmed leading to around 59,170 deaths have been recorded world-over. This article studies multiple countries-based

COVID-19 or SARS-Cov-2, affecting 6 million people and more than 300,000 deaths, the global pandemic has engulfed more than 90% countries of the world. The virus started from a single organism and is escalating at a rate of 3% to 5% daily and seems to be a never ending process. Understanding the basic dynamics and presenting new predictions models for evaluating the potential effect of the virus is

In this paper, a discrete-time SEIR measles epidemic model with fractional-order and constant vaccination is investigated. The basic reproduction number with an algebraic criterion are used to study the local asymptotic stability of the equilibrium points. Two types of codimension one bifurcation namely, flip and Neimark-Sacker (N-S) bifurcations and their intersection codimension two flip-N-S bifurcation

The novel Covid-19 was identified in Wuhan China in December, 2019 and has created medical emergency world wise and distorted many life in the couple of month, it is being burned challenging situation for the medical scientist and virologists. Fractional order derivative based modeling is quite important to understand the real world problems and to analyse realistic situation of the proposed model

This paper deals with the impact of two discrete-time delays on the basic Goodwin growth cycle model. The former concerns the existence of a finite time delay for building capital goods as suggested by Kalecki. The latter pertains to the wage lag hypothesis. This is because, taking the current change of the employment rate into account, workers and capitalists bargain new wage periodically. There are

Reservoir computing (RC) is a brain-inspired computing framework that employs a transient dynamical system whose reaction to an input signal is transformed to a target output. One of the central problems in RC is to find a reliable reservoir with a large criticality, since computing performance of a reservoir is maximized near the phase transition. In this work, we propose a continuous reservoir that

Using the algebraic approach Lie symmetries, we spin new infinitesimals for the (4+1) Fokas equation that admits an infinite number of possibilities for its Lie vectors. Through the commutation product between the unknown vectors, we generate a system of ordinary differential equations (ODEs). By solving this system, we explore these infinitesimals. Through four stages of the similarity reduction using

In linear science, the wave motion equation with general D’Alembert wave solutions is one of the fundamental models. The D’Alembert wave is an arbitrary travelling wave moving along one direction under a fixed model (material) dependent velocity. However, the D’Alembert waves are missed when nonlinear effects are introduced to wave motions. In this paper, we study the possible travelling wave solutions

In this paper, a non-linear mathematical model for HIV-TB co-infection has been proposed. A constant time delay parameter is introduced into the model which accounts for the delay in detection and the commencement of appropriate treatment for co-infected individuals. The basic reproduction number along with the location and existence of equilibrium points is computed. Local stability analysis of all

The novel coronavirus (COVID-19) has significantly spread over the world and comes up with new challenges to the research community. Although governments imposing numerous containment and social distancing measures, the need for the healthcare systems has dramatically increased and the effective management of infected patients becomes a challenging problem for hospitals. Thus, accurate short-term forecasting

Homeodynamic system (HS) in the biological studies (from the Greek homoios (similar) and Dynamis (energy)) designates the accommodating instruments of stabilizing and repairing of the fundamental reliability and functional efficiency of living schemes. In this effort, we employ the concept of conformable calculus (CC) to generalize the homeodynamic system. The generalization requires a controller in

In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate

The pandemic transition is a hallmark of current epidemiological models, predicting a continuous shift from a healthy to a pandemic state, whose critical point is driven by the parameters of the disease, e.g., its infection, recovery or mortality rates. These parameters, characterizing the disease cycle, are tuned by the biological characteristics of the pathogen, capturing its natural time-scales

We employ deep learning to propose an Artificial Neural Network (ANN) based and data stream guided real-time incremental learning algorithm for parameter estimation of a non-intrusive, intelligent, adaptive and online analytical model of Covid-19 disease. Modeling and simulation of such problems poses an additional challenge of continuously evolving training data in which the model parameters change

This work employed extended auxiliary equation approach to secure soliton solutions to magneto–optic waveguides that maintains Kudryashov’s law of refractive index. First, solutions in terms of Jacobi’s elliptic functions are obtained and subsequently upon carrying out the limiting operations when the modulus of ellipticity approaches zero or unity, bright, dark or singular soliton solutions are revealed

The COrona VIrus Disease (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV2) has resulted in a challenging number of infections and deaths worldwide. In order to combat the pandemic, several countries worldwide enforced mitigation measures in the forms of lockdowns, social distancing, and disinfection measures. In an effort to understand the dynamics of this

Fractional Brownian motion (FBM) is related to the notions of self-similarity, ergodicity and long memory. These properties have made FBM important in modeling real-world phenomena in different experiments ranging from telecommunication to biology. However, these experiments are often disturbed by a noise which source can be, e.g., the instrument error. In this paper we propose a rigorous statistical

The main idea of this paper is to establish the novel fractional Gegenbauer functions (FGFs) for solving three kinds of fractional differential equations generated by the variable-order fractional derivatives in the Atangana-Baleanu-Caputo (ABC) sense. The numerical scheme is discussed based on the modified operational matrices (MOMs) of Atangana-Baleanu variable-order (AB-VO) fractional integration

We study the integrability of a Hamiltonian system proposed recently by Maciejewski and Przybylska, and which constitutes an extension of one studied (and integrated) by Lagrange. While the previous authors used the differential Galois theory formalism in order to study the integrability of this extended Hamiltonian, we approach the problem from the point of view of singularity analysis. For all values

Coronavirus is an epidemic that spreads very quickly. For this reason, it has very devastating effects in many areas worldwide. It is vital to detect COVID-19 diseases as quickly as possible to restrain the spread of the disease. The similarity of COVID-19 disease with other lung infections makes the diagnosis difficult. In addition, the high spreading rate of COVID-19 increased the need for a fast

The novel coronavirus disease 2019 (COVID-19), detected in Wuhan City, Hubei Province, China in late December 2019, is rapidly spreading and affecting all countries in the world. Real-time reverse transcription-polymerase chain reaction (RT-PCR) test has been described by the World Health Organization (WHO) as the standard test method for the diagnosis of the disease. However, considering that the

COVID-19 blocked Wuhan in China, which was sealed off on Chinese New Year's Eve. During this period, the research on the relevant topics of COVID-19 and emotional expressions published on social media can provide decision support for the management and control of large-scale public health events. The research assisted the analysis of microblog text topics with the help of the LDA model, and obtained

Nowadays, a significant number of infectious diseases such as human coronavirus disease (COVID-19) are threatening the world by spreading at an alarming rate. Some of the literatures pointed out that the pandemic is exhibiting seasonal patterns in its spread, incidence and nature of the distribution. In connection to the spread and distribution of the infection, scientific analysis that answers the

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked

In this paper, we extend a nutrient-phytoplankton model with viral infection from a deterministic model to a stochastic model by introducing white noise and color noise. We analyze this model mainly from the perspectives of mathematics and biology. Mathematically, we get a critical value. In the case of low white noise intensity, if this critical value is less than one, the infected phytoplankton tend