Efficient Digital Realization of Endocrine Pancreatic ß-Cells.

The accurate implementation of biological neural networks, which is one of the important areas of research in the field of neuromorphic, can be studied in the case of diseases, embedded systems, the study of the function of neurons in the nervous system, and so on. The pancreas is one of the main organs of human that performs important and vital functions in the body. One part of the pancreas is an endocrine gland and produces insulin, while another part is an exocrine gland that produces enzymes for digesting fats, proteins and carbohydrates. In this paper, an optimal digital hardware implementation for pancreatic ß-cells, which is the endocrine type, is presented. Since the equations of the original model include nonlinear functions, and the implementation of these functions results in greater use of hardware resources as well as deceleration, to achieve optimal implementation, we have approximated these nonlinear functions using the base-2 functions and LUT. The results of dynamic analysis and simulation show the accuracy of the proposed model compared to the original model. Analysis of the synthesis results of the proposed model on the Spartan-3 XC3S50 (5TQ144) reconfigurable board (FPGA) shows the superiority of the proposed model over the original model. These advantages include using fewer hardware resources, a performance almost twice as fast, and 19% less power consumption, than the original model.

On fractional approaches to the dynamics of a SARS-CoV-2 infection model including singular and non-singular kernels.

Covid-19 (2019-nCoV) disease has been spreading in China since late 2019 and has spread to various countries around the world. With the spread of the disease around the world, much attention has been paid to epidemiological knowledge. This knowledge plays a key role in understanding the pattern of disease transmission and how to prevent a larger population from contracting it. In the meantime, one should not overlook the significant role that mathematical descriptions play in epidemiology. In this paper, using some known definitions of fractional derivatives, which is a relatively new definition in differential calculus, and then by employing them in a mathematical framework, the effects of these tools in a better description of the epidemic of a SARS-CoV-2 infection is investigated. To solve these problems, efficient numerical methods have been used which can provide a very good approximation of the solution of the problem. In addition, numerical simulations related to each method will be provided in solving these models. The results obtained in each case indicate that the used approximate methods have been able to provide a good description of the problem situation.

A fractional system of delay differential equation with nonsingular kernels in modeling hand-foot-mouth disease.

In this article, we examine a computational model to explore the prevalence of a viral infectious disease, namely hand-foot-mouth disease, which is more common in infants and children. The structure of this model consists of six sub-populations along with two delay parameters. Besides, by taking advantage of the Atangana-Baleanu fractional derivative, the ability of the model to justify different situations for the system has been improved. Discussions about the existence of the solution and its uniqueness are also included in the article. Subsequently, an effective numerical scheme has been employed to obtain several meaningful approximate solutions in various scenarios imposed on the problem. The sensitivity analysis of some existing parameters in the model has also been investigated through several numerical simulations. One of the advantages of the fractional derivative used in the model is the use of the concept of memory in maintaining the substantial properties of the understudied phenomena from the origin of time to the desired time. It seems that the tools used in this model are very powerful and can effectively simulate the expected theoretical conditions in the problem, and can also be recommended in modeling other computational models in infectious diseases.

On the modeling of the interaction between tumor growth and the immune system using some new fractional and fractional-fractal operators.

Humans are always exposed to the threat of infectious diseases. It has been proven that there is a direct link between the strength or weakness of the immune system and the spread of infectious diseases such as tuberculosis, hepatitis, AIDS, and Covid-19 as soon as the immune system has no the power to fight infections and infectious diseases. Moreover, it has been proven that mathematical modeling is a great tool to accurately describe complex biological phenomena. In the recent literature, we can easily find that these effective tools provide important contributions to our understanding and analysis of such problems such as tumor growth. This is indeed one of the main reasons for the need to study computational models of how the immune system interacts with other factors involved. To this end, in this paper, we present some new approximate solutions to a computational formulation that models the interaction between tumor growth and the immune system with several fractional and fractal operators. The operators used in this model are the Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo in both fractional and fractal-fractional senses. The existence and uniqueness of the solution in each of these cases is also verified. To complete our analysis, we include numerous numerical simulations to show the behavior of tumors. These diagrams help us explain mathematical results and better describe related biological concepts. In many cases the approximate results obtained have a chaotic structure, which justifies the complexity of unpredictable and uncontrollable behavior of cancerous tumors. As a result, the newly implemented operators certainly open new research windows in further computational models arising in the modeling of different diseases. It is confirmed that similar problems in the field can be also be modeled by the approaches employed in this paper.

On forecasting the spread of the COVID-19 in Iran: The second wave.

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 of many people around the world. In this research, we are interested in analyzing the existing data to predict the number of infected people in the second wave of out-breaking COVID-19 in Iran. For this purpose, a model is proposed. The mathematical analysis corresponded to the model is also included in this paper. Based on proposed numerical simulations, several scenarios of progress of COVID-19 corresponding to the second wave of the disease in the coming months, will be discussed. We predict that the second wave of will be most severe than the first one. From the results, improving the recovery rate of people with weak immune systems via appropriate medical incentives is resulted as one of the most effective prescriptions to prevent the widespread unbridled outbreak of the second wave of COVID-19.

Coronavirus pandemic: A predictive analysis of the peak outbreak epidemic in South Africa, Turkey, and Brazil.

In this research, we are interested in predicting the epidemic peak outbreak of the Coronavirus in South Africa, Turkey, and Brazil. Until now, there is no known safe treatment, hence the immunity system of the individual has a crucial role in recovering from this contagious disease. In general, the aged individuals probably have the highest rate of mortality due to COVID-19. It is well known that this immunity system can be affected by the age of the individual, so it is wise to consider an age-structured SEIR system to model Coronavirus transmission. For the COVID-19 epidemic, the individuals in the incubation stage are capable of infecting the susceptible individuals. All the mentioned points are regarded in building the responsible predictive mathematical model. The investigated model allows us to predict the spread of COID-19 in South Africa, Turkey, and Brazil. The epidemic peak outbreak in these countries is considered, and the estimated time of the end of infection is regarded by the help of some numerical simulations. Further, the influence of the isolation of the infected persons on the spread of COVID-19 disease is investigated.

A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence.

The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.

Numerical solution of predator-prey model with Beddington-DeAngelis functional response and fractional derivatives with Mittag-Leffler kernel.

One of the major applications of the nonlinear system of differential equations in biomathematics is to describe the predator-prey problem. In this framework, the fractional predator-prey model with Beddington-DeAngelis is examined. This model is formed of three nonlinear ordinary differential equations to describe the interplay among populations of three species including prey, immature predator, and mature predator. The fractional operator used in this model is the Atangana-Baleanu fractional derivative in Caputo sense. We show first that the fractional predator-prey model has a unique solution, then propose an efficient numerical scheme based on the product integration rule. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results. The numerical method used in this paper can be utilized to solve other similar models.

Analysis of two avian influenza epidemic models involving fractal-fractional derivatives with power and Mittag-Leffler memories.

Since certain species of domestic poultry and poultry are the main food source in many countries, the outbreak of avian influenza, such as H7N9, is a serious threat to the health and economy of those countries. This can be considered as the main reason for considering the preventive ways of avian influenza. In recent years, the disease has received worldwide attention, and a large variety of different mathematical models have been designed to investigate the dynamics of the avian influenza epidemic problem. In this paper, two fractional models with logistic growth and with incubation periods were considered using the Liouville-Caputo and the new definition of a nonlocal fractional derivative with the Mittag-Leffler kernel. Local stability of the equilibria of both models has been presented. For the Liouville-Caputo case, we have some special solutions using an iterative scheme via Laplace transform. Moreover, based on the trapezoidal product-integration rule, a novel iterative method is utilized to obtain approximate solutions for these models. In the Atangana-Baleanu-Caputo sense, we studied the uniqueness and existence of the solutions, and their corresponding numerical solutions were obtained using a novel numerical method. The method is based on the trapezoidal product-integration rule. Also, we consider fractal-fractional operators to capture self-similarities for both models. These novel operators predict chaotic behaviors involving the fractal derivative in convolution with power-law and the Mittag-Leffler function. These models were solved numerically via the Adams-Bashforth-Moulton and Adams-Moulton scheme, respectively. We have performed many numerical simulations to illustrate the analytical achievements. Numerical simulations show very high agreement between the acquired and the expected results.

The convergence study of the homotopy analysis method for solving nonlinear Volterra-Fredholm integrodifferential equations.

We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.

An analytical study for (2 + 1)-dimensional Schrödinger equation.

In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.