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The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (‘[Formula: see text]’) to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model's solution by employing the Laplace transform approach to solve the fractional Gronwall's inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model's basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak.

This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public knowledge. The findings might improve healthcare budget apportionment, public health policy, and contest Ebola and related infections. In this study, we fully observe the new model SEIHR that we have constructed. We start by outlining the essential concepts of the model and confirming its mathematical reliability. Next, we calculate the fundamental reproductive number (R0), which is critical for appreciating how the infection spreads and how effective treatments might be. We also study stability analysis, which looks at when the disease may decline or become chronic. Furthermore, we exhibit the occurrence of bifurcation in the EVD Epidemic Model and perform a sensitivity analysis of (R0). The main findings of this study show that for R0<1, the disease-free equilibrium, is globally stable, meaning the disease will die out, whereas for R0>1, the endemic equilibrium is stable, meaning the disease persists. Additionally, the sensitivity analysis reveals that the most influential parameters in controlling R0 are the transmission rate and the recovery rate, which could guide effective intervention strategies. Finally, we use numerical simulations so that out outcomes are more significant.

The SEIQHR model, introduced in this study, serves as a valuable tool for anticipating the emergence of various infectious diseases, such as COVID-19 and illnesses transmitted by insects. An analysis of the model’s qualitative features was conducted, encompassing the computation of the fundamental reproduction number, R0. It was observed that the disease-free equilibrium point remains singular and locally asymptotically stable when R01. Additionally, specific conditions were outlined to guarantee the local asymptotic stability of both equilibrium points. Employing numerical simulations, the graphical representation illustrated the influence of model parameters on disease dynamics and the potential for its eradication across different noninteger orders of the Caputo derivative. In essence, the adoption of a fractional epidemic model contributes to a deeper comprehension and enhanced biological insights into the dynamics of diseases.

In this article, we introduce and analyze a novel fractal-fractional chaotic system. We extended the memristor-based chaotic system to the fractal-fractional mathematical model using Atangana-Baleanu–Caputo and Caputo-Fabrizio types of derivatives with exponential decay type kernels. We established the uniqueness and existence of the solution through Banach's fixed theory and Schauder's fixed point. We used some new numerical methods to derive the solution of the considered model and study the dynamical behavior using these operators. The numerical simulation results presented in both cases include the two and three-dimensional phase portraits and the time-domain responses of the state variables to evaluate the efficacy of both kernels.

The Covid illness (COVID-19), which has emerged, is a highly infectious viral disease. This disease led to thousands of infected cases worldwide. Several mathematical compartmental models have been examined recently in order to better understand the Covid disease. The majority of these models rely on integer-order derivatives, which are incapable of capturing the fading memory and crossover behaviour observed in many biological phenomena. Similarly, the Covid disease is investigated in this paper by exploring the elements of COVID-19 pathogens using the non-integer Atangana-Baleanu-Caputo derivative. Using fixed point theory, we demonstrate the existence and uniqueness of the model's solution. All basic properties for the given model are investigated in addition to Ulam-Hyers stability analysis. The numerical scheme is based on Lagrange's interpolation polynomial developed to estimate the model's approximate solution. Using real-world data, we simulate the outcomes for different fractional orders in Matlab to illustrate the transmission patterns of the present Coronavirus-19 epidemic through graphs.

In this article, the Caputo fractional derivative operator of different orders 0

In this paper, a stochastic HIV/AIDS epidemic model has been studied numerically. A discussion among the solutions related to deterministic HIV/AIDS model and stochastic HIV/ AIDS epidemic model has shown that the stochastic solution is more realistic than the deterministic solution. To control the diseases, the threshold parameter R0 plays a key role in the stochastic HIV/AIDS epidemic model. If R01. The explicit approaches such as the Milstein scheme, stochastic Euler scheme, and stochastic Runge-Kutta 4 are dependent on temporal step size, whereas non-standard finite difference approaches are independent of step size. The results for numerical approaches like the Milstein scheme, stochastic Euler scheme, and stochastic Runge-Kutta 4 scheme fail for outsized step size. The stochastic non-standard finite difference scheme conserves dynamic features like confinedness, consistency and positivity.

Abstract Infection of hepatitis B virus (HBV) is a global health problem. We provide the study about hepatitis B virus dynamics that can be controlled by education campaign (awareness), vaccination, and treatment. Initially we bring constant controls in considerations for treatment, vaccination, and education campaign (awareness). In the case of constant controls, we study the stability and existence of the disease-free and endemic equilibria model’s solutions. Afterwards, we take time as a control and formulate the suitable optimal control problem, acquire optimal control strategy in order to reduce the number of humans that are infected and the costs associated. At the end, results of numerical simulations show that the optimal combination of education campaign (awareness), treatment, and vaccination is the most efficient way to control the infection of hepatitis B virus (HBV) infection.

Abstract In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We find that the fractional-order brushless DC motor system exhibits the character of chaos. For the proposed system, we show the largest exponent to be 0.711625. We calculate the equilibrium points of the model and discuss their local stability. We apply an iterative scheme by using the Laplace transform to find a special solution in this case. By taking into account the rule of trapezoidal product integration we develop two iterative methods to find an approximate solution of the system. We also study the existence and uniqueness of solutions. We take into account the numerical solutions for Caputo Liouville product integration and Atangana–Baleanu Caputo product integration. This scheme has an implicit structure. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results.

In this article, a non-integer nonlinear mathematical model for toxoplasmosis disease in human and cat population is proposed and studied. The basic concepts of the model's dynamic are given. The study of qualitative dynamics is done by the basic threshold parameter $ R_{0} $ . Local and global stabilities are done and the system's disease free equilibrium point is an attractor when $ R_{0}1 $ . The sensitivity analysis of $ R_{0} $ shows which parameter has positive/negative impact on the model. Numerical simulation of the model for the parameters occurred in threshold parameter is also discussed. The techniques of Adams Bashforth Moulton will be considered to justify all the derived theoretical results which will help in understanding to study the effect of various parameters to both the transient and steady-state dynamics of the disease infection.

This paper represents a non-integer-order Vallis systems in which we applied the Grünwald-Letnikov tactics with Binomial coefficients in order to realize the numerical simulations to a set of equations. Recently researchers reported in the literature that it is the generalization of integer order dynamical model. Several cases involving non-integer and integer analysis with different values of non-integer order have been applied to Vallis systems to see the behavior of simulations. To visualize the effect of non-integer order approach, the time histories and phase portraits have been plotted. The consequences expose that the non-integer-order Vallis model can reveal a genuine equitable comportment to Vallis systems and might bid greater perceptions towards the understanding of such complex dynamic systems.

Abstract In this paper, a nonlinear mathematical model with diffusion is taken into account to review the dynamics of Lengyel–Epstein chemical reaction model to describe the oscillating chemical reactions. For this purpose, the dimensionless Lengyel–Epstein model with diffusion and homogeneous boundary condition is considered. The steady states with and without diffusion of the Lengyel–Epstein model are studied. The basic reproductive number is computed and the global steady states for the system are calculated. Numerical results are offered for two systems using three well known techniques to validate the main outcomes. The consequences established from this qualitative study are supported by numerical simulations characterized by distinct programs, adopting forward Euler method, Crank–Nicolson method, and nonstandard finite difference method.

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.

This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution’s existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model’s endemic and disease-free equilibrium points for local and global stability. Furthermore, we find approximate solutions for the non-linear fractional model using the Modified Euler Method (MEM). To support analytical findings, numerical simulations are carried out.

In this article, the Adomian decomposition method (ADM) is applied to find the solution of HIV infection model of latently infected CD4+T cells. This method investigates the solution of ordinary differential equation which is calculated in the form of the components of an infinite series. These components can be easily calculated. The efficiency and the reliability of proposed method is demonstrated in different time intervals by numerical example. The derived results indicate that the approximate solution by using the ADM can be obtained in a more efficient way. All computations have been carried out by computer code written in Mathematica.

Abstract In this manuscript, we investigate some appropriate conditions which ensure the existence of at least one solution to a class of fractional order differential equations (FDEs) provided by { − C D q z ( t ) = θ ( t , z ( t ) ) ; t ∈ J = [ 0 , 1 ] , q ∈ ( 1 , 2 ] , z ( t ) | t = 0 = ϕ ( z ) , z ( 1 ) = δ C D p z ( η ) , p , η ∈ ( 0 , 1 ) . $$\textstyle\begin{cases} -{}^{C}\mathbf{D}^{q} z(t)=\theta (t,z(t)); \quad t\in \mathfrak{J}=[0,1], q\in (1, 2], \\ z(t)\vert _{t=0}=\phi (z),\qquad z(1)=\delta{}^{C}\mathbf{D}^{p} z(\eta ),\quad p, \eta \in (0,1). \end{cases} $$ The nonlinear function θ : J × R → R $\theta :\mathfrak{J}\times \mathbf{R} \rightarrow \mathbf{R}$ is continuous. Further, δ ∈ ( 0 , 1 ) $\delta \in (0, 1)$ and ϕ ∈ C ( J , R ) $\phi \in C(\mathfrak{J},\mathbf{R})$ is a non-local function. We establish some adequate conditions for the existence of at least one solution to the considered problem by using Grönwall’s inequality and a priori estimate tools called the topological degree method. We provide two examples to verify the obtained results.

This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model.

The Kurdish speech community in Iraq, autonomous since 1991, has witnessed an important situation of multilingualism due to the existence of a large number of refugees (more than two million). On the other hand, in spite of the official status of the Kurdish language in Iraq, the Kurds in this country have not yet managed to unify a Kurdish standard language, having the same use in education systems and Kurdish media. How do the Kurds of Iraq, whose language is widely considered as the essential element in their national identity, contribute today to the assertion and protection of this identity ? To be able to answer this question, this article will lean on the data which we collected within the framework of our memory during the Master's program in 2013, during a survey led with the Kurds of Iraq. The latter worried about the current situation of their language within their society. They demanded the Kurdish government and the Kurdish academy to give more importance to the question of the kurdish language and its development to better protect the Kurdish national identity.

The phosphate ions adsorption of some calcarious soils of Nainawa and Kirkuk regions from 0.01 M KCL solution containing (1-12) micromoles P has been studied .The different type of soils (32.4-39.84) % CaCO3 were fertilized with (22.5, 45, 90) kg P/ha and planted with maize ( Zea mays L. ) in 1 kg pots for five years. Adsorbed phosphorous at equilibrium solution concentration of 0.2 ppm P ( Ce = 0.2ppm P ) was determind .It was established an inverse relation between adsorbed P at Ce = 0.2 ppm P and the extractable phosphorous was established. The amount of adsorbed phosphorous at Ce = 0.2 ppm P diminished as the rate of applied fertilizers increase. From the data obtained in this study one may conclude that for the studied soils an average of 69.3 ppm extractable P correspond to an equilibrium soil solution of 0.2 ppm P ( Ce = 0.2 ppm P ) considered as adequate nutration level for most field crops, and justifies the use of P adsorption isotherms for evaluating the phosphorous fertilizer requirement.

The economy of any state cannot exist in isolation and needs investments, both external and internal. Only by creating suitable conditions for attracting investment, the state will ultimately be able to boast of the accelerated rates of development of all sectors of the economy. This article examines the role and importance of marketing in investing in the non-oil sector. The author reveals the essence of investment marketing, presents the elements of the marketing complex in relation to enterprises that have set themselves the goal of attracting investors.