numerical simulation

In this paper, applying Caputo fractional derivative operator, the SCIRS epidemic model of Covid-19 has been presented. First, the well-definedness of the model (positive invariance) has been checked. We then calculate the equilibrium points of the system and the reproduction number and discuss the local and global stability of the equilibria based on values of the reproduction number. For the global stability of the rest points, the Liapunov’s second method and LaSalle’s invarianceprinciple are used. Applying fixed point theory, the existence and uniqueness of the solutions of the model has been proven. Additionally, by using MATLAB and fractional Euler method, a numerical method has been applied to simulate the solutions based on real data and predict the transmission of Covid-19.

The applications of a Reaction-Diffusion boundary value problems are found in science, biochemical applications, and chemical applications. The Ananthaswamy-Sivasankari method (ASM) is employed to solve the considered specific models like non-linear reaction-diffusion model in porous catalysts, spherical catalysts pellet, and catalytic reaction-diffusion process in a catalyst slab. An accurate semi-analytical expression for the concentrations and effectiveness factors are given in the explicit form. Graphical representations are used to display the impacts of several parameters, including the Thiele modulus, characteristic reaction rate, concentration of half-saturation, reaction order and dimensionless constant in Langmuir-Hinshelwood kinetics. The impact of numerous parameters namely the Langmuir-Hinshelwood kinetics and Thiele modulus on effectiveness factors are displayed graphically. Our semi-analytical findings shows good match in all parameters when compared to numerical simulation using MATLAB. Many non-linear problems in chemical science especially, the Reaction-Diffusion equations, Michaelis-Menten kinetic equation, can be resolved with the aid of the new approximate analytical technique, ASM.

Atherosclerosis is one of the most common diseases in the world. Med-ication with metal stents plays an important role in treating this disease. There are many models for delivering drugs from stents to the arterial wall. This paper presents a model that describes drug delivery from the stent coating layers to the arterial wall tissue. This model complements the previous models by considering the mec hanical properties of the arte-rial wall tissue, which changes due to atherosclerosis and improves results for designing stents. The stability behavior of the model is analyzed, and a number of numerical results are provided with explanations. A compar-ison between numerical and experimental results, which examine a more accurate match between the in vivo and in vitro, is shown.

The objectives of this study are to develop the SEIR model for COVID-19 and evaluate its main parameters such as therapeutic vaccines, vaccination rate, and effectiveness of prophylactic. Global and local stability of the model and numerical simulation are examined. The local stability of equilibrium points was classified. A Lyapunov function is constructed to analyze the global stability of the disease-free equilibrium. The simulation part is based on two situations, including the USA and Iran. Our results provide a good contribution to the current research on this topic.

In this paper, we present a numerical simulation for integrating active load control using corona discharge-based plasma actuators on the trailing edge of a wind turbine blade. Eulerian simulation is done on a 660 kW wind turbine blade with NACA 0012 profile. The electrohydrodynamic incompressible flow created between two electrodes using the combination of the EHDFoam solver with the BoyantPimpleFoam solver is carried out in the free and open-access OpenFOAM software. The results have been validated using numerical and experimental work. The effects of environmental parameters such as temperature, relative humidity and environmental pressure on the corona discharge process have been investigated. The results of this research showed that with the increase in temperature, humidity and pressure, the discharge process is decreased. The results show a 62% and 35% decrease in the average transfer momentum with an increase in relative humidity and temperature, respectively.

In this study, a modified model of HIV with therapeutic and preventive controls is developed. Moreover, a simple evaluation of the optimal control problem is investigated. We construct the Hamiltonian function by way of integrating Pontryagin’s maximal principle to achieve the point-wise optimal solution. The effects obtained from the version analysis strengthen public health education to a conscious population, PrEP for early activation of HIV infection prevention, and early treatment with artwork for safe life after HIV infection. Moreover, numerical simulations are done using the MATLAB platform to illustrate the qualitative conduct of the HIV infection. In the end, we receive that adhering to ART protective prone people, the usage of PrEP along with different prevention control is safer control measures.

In this research, we aim to analyze a mathematical model of Maize streak virus disease as a problem of fractional optimal control. For dynamical analysis, the boundedness and uniqueness of solutions have been investi-gated and proven. Also, the basic reproduction number is obtained, and local stability conditions are given for the equilibrium points of the model. Then, an optimal control strategy is proposed for the purpose of examining the best strategy to fight the maize streak disease. We solve the fractional optimal control problem by a forward-backward sweep iterative algorithm. In this algorithm, the state variable is obtained in a forward and co-state variable by a backward method where an explicit Runge-Kutta method is used to solve differential equations arising from fractional optimal control problems. Some comparative results are presented in order to verify the model and show the efficacy of the fractional optimal control treatments.

Various methods are used to improve the heat transfer coefficient of fluids flow inside the various cross-sections of channels, and one of these methods is the use of porous media (PM) in various engineering and industrial applications such as heat exchangers and storage tanks for solar energy. This research paper shows a numerical study using the COMSOL Multiphysics 6.0 program, the effect of the PM (Glass Spheres) inside a square-shaped channel (12 * 12 cm2) by taking three different locations of the PM for two cases (constant heat flux, and constant wall temperature) at the lower surface of a test section and knowing their effect on the distribution of temperature, and velocity to compare them with the absence of the PM for the same channel. The results showed the best temperature distribution to get the best heat transfer coefficient and thus increase the Nusselt number in position (1) of the PM for the test section.

Covid-19 disease is a respiratory illness caused by SARS-Cov-2 and poses a serious public health risk. It usually spread from person-to-person. The fractional- order of covid-19 was determined and basic reproduction number using the next generation matrix was calculated. The stability of disease-free equilibrium and endemic equilibrium of the model were investigated. Also, sensitivity analysis of the reproduction number with respect to the model parameters were carried out. It was observed that in the absence of infected persons, disease free equilibrium is achievable and is asymptotically stable.Numerical simulations were presented graphically. The results of the model analysis indicated that $R_{0}$ $\mathrm{<}$ 1 is adequate enough to reducing the spread of disease and disease persevere in the population when $R_{0}$ $\mathrm{>}$ 1 The numerical results showed that effective vaccination of the population helps in curtailing the spread of the viral disease.In order to know whether the disease may die out or persist, basic reproduction number, $R_{0}$ was obtained using Next Generation Matrix Method. It was observed that the value of $R_{0}$ is high when the depletion of awareness programme is high while the value of $R_{o}$ is very low when the rate of implementation of awareness programme is high. So, neglecting the implementation of awareness program can have serious effect on the population. The model shows the implementation of awareness program is the key eradication to the pandemic.

Fish stocks in the developing world are often depleted as a result of the application of excessive fishing effort on the part of the fishermen. A bioeconomic model with logistic growth, proportional harvesting and quadratic costs is proposed to study the effect of overcapacity on a marine fishery. Also incorporated into the model is an isoperimetric constraint to account for the annual total allowable catch (TAC). Pontryagin's maximum principle is employed to determine the necessary conditions for optimality of the model. Additionally, the sufficiency conditions that guarantee the existence and uniqueness of the optimality system are discussed. Furthermore, the relationship between the shadow price of fish stock, the shadow price of the total allowable catch and the marginal net revenue as it relates to the optimal fishing effort is explored. Numerical simulation with empirical data on the Ghana sardinella fishery is performed to validate the theoretical results. The findings of the study indicate that for a TAC equal to the maximum sustainable yield (MSY), the average fishing effort should not exceed $95\%$ of the MSY effort, provided that the initial stock size is exactly 55% of the carrying capacity.

A human host-mosquito vector model for transmission of malaria with infow of infected immigrants is formulated. The mosquito population includes aquatic stages (eggs, larvae, and pupae) and mature stages which have highly temperature and rainfall dependent life cycles. Model analysis reveals that the model only attains two (2) endemic equilibria; one in absence of the vector population and the other in presence of the vector population. The endemic equilibrium without the mosquito vector population is unstable. The endemic equilibrium with the vector population is locally stable and globally unstable. Numerical simulations of the model reveal that the proportion of infected humans introduced into the community does not significantly change the pattern of malaria transmission.

In this paper, the nonlinear dynamical system modeling the effect of awareness program by media on spread of infectious disease is considered. The model is mathematically formulated by the deterministic compartmental model consisting of susceptible population, infected population, aware population and cumulative density of awareness spread by the media. Homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the exact solution or enabling to built the approximate solution of the problem. Numerical solutions are obtained and the results are discussed graphically using Maple. The method allows to determine the solution in form of the continuous function, and shows the significance of awareness program driven by media in spread of an infectious disease, but due to immigration, the disease may remain endemic . The simulation analysis of the model with different parameter values confirms the analytical results.

The rapid spread of coronavirus disease (COVID-19) has increased the attention to the mathematical modeling of spreading the disease in the world. The behavior of spreading is not deterministic in the last year. The purpose of this paper is to present a stochastic differential equation for modeling the data sets of the COVID-19 involving infected, recovered, and dead cases. At first, the time series of the covid-19 is modeled with the Ornstein-Uhlenbeck process and then using the Ito lemma and Euler approximation the analytical and numerical simulations for the stochastic differential equations are achieved. Parameters estimation is done using the maximum likelihood estimator. Finally, numerical simulations are performed using reported data by the world health organization for case studies of Italy and Iran. The numerical simulations and root mean square error criteria confirm the accuracy and efficiency of the findings of the present study.

Tungiasis is a zoonosis affecting human beings and a broad range of domestic and syvatic animals caused by the penetration of an ectoparasite known as “Tunga penetrans” into the skin of its host. In this paper we derive and analyze a mathematical model of control measures and then examine the effect of the control strategies on the transmission dynamics of Tungiasis. The model effective reproduction number is determined using the next generation operator method and the analysis is performed using the stability theory of the differential equations. The analytical results show that the disease free equilibrium is locally asymptotically stable when and unstable when . Using Meltzer matrix stability theorem we found that the disease free equilibrium is globally asymptotically stable and by Lyapunov method, the endemic equilibrium is globally asymptotically stable when . From the numerical simulation it was observed that the control strategies have positive impact on the reduction of transmission of Tungiasis disease and that they work better in combination than when applied as singly. The results from simulations will help the decision makers from national health care to advise people at risk with Tungiasis to apply the control strategies based on: educational campaign, personal protection, personal treatment, environmental hygiene and insecticides application to control the flea.

This work is devoted to study of  the stability analysis of generalized fractional nonlinear system including the regularized Prabhakar derivative. We present several criteria for the generalized Mittag-Leffler stability and the asymptotic stability of this system by using the Lyapunov direct method. Further, we provide two test cases to illustrate the effectiveness  of  results. We apply the numerical method to solve the generalized fractional system with the regularized Prabhakar fractional systems and reveal asymptotic stability behavior of the presented systems by employing numerical simulation.

In this work, a researcher develop $SHEIQRD$ (Susceptible-Stay at home-Exposed-Infected-Quarantine-Recovery-Death) coronavirus pandemic spread model. The disease-free and endemic equilibrium points are calculated and analyzed. The basic reproductive number $R_0$ is derived and its sensitivity analysis is done. COVID-19 pandemic spread is die out when $R_0leq 1$ and its persist in the community whenever $R_0>1$. More than $10%$ of lockdown or home quarantine, above $50%$ and $30%$ identification and isolation of expose and infected individuals respectively, and reduction home quarantine return rate(less than $10%$) can be mitigates the pandemics. Finally, theoretical analysis and numerical results are consistent.

The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the exact solution or enabling to built the approximate solution of the problem. Numerical solutions are obtained and the results are discussed graphically. The method allows to determine the solution in form of the continuous function, which is significant for the analysis of the steady state dimensionless substrate concentration with dimensionless distance on the different support materials.