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We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter τ concerns the effects of time delay and we demonstrate that the locally asymptotic stability holds for the present equilibrium. The reproduction number is brief in less than or greater than one, and it effectively is controlling the COVID-19 infection outbreak and subsequently reveals insight into understanding the patterns of the flare-up. We have included eight parameters and the least square method allows us to estimate the initial values for the Indian COVID-19 pandemic from real-life data. It is one of India’s current pandemic models that have been studied for the time being. This Covid19 SEIR model can apply with or without delay to all country’s current pandemic region, after estimating parameter values from their data. The sensitivity of seven parameters has also been explored. The paper also examines the impact of immune response time delay and the importance of determining essential parameters such as the transmission rate using sensitivity indices analysis. The numerical experiment is calculated to illustrate the theoretical results.

Anti-viral therapy is comparatively very effective for patients who get affected by the hepatitis B virus. It is of prime importance to understand the different relations among the viruses, immune responses and overall health of the liver. In this paper, mathematical modeling is done to analyze and understand the effect of antiviral therapy using LHAM which describes the possible relation to HBV and target liver cells. The numerical simulations and error analysis are done up to a sixth-order approximation with the help of Matlab. This paper analyzes how the number of infected cells largely gets reduced and also how the liver damage can be controlled. Therefore, the treatment is successful for HBV infected patients.

A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic reproduction ratio $R_{0}$ R 0 is derived. This reveals that $R_{0} < 1$ R 0 < 1 is locally asymptotically stable in the viral free steady state, and the infected steady state condition remains locally asymptotically stable with $R_{0} > 1$ R 0 > 1 in the absence of a delay in the immune response. Moreover, the existence of Hopf bifurcation with CTL response delay is demonstrated. The estimation of delay length is used to maintain stability. Numerical simulations are implemented to explain the mathematical results.

Hepatitis B virus (HBV) is a life-threatening virus that causes very serious liver-related diseases from the family of Hepadnaviridae having very rare qualities resembling retroviruses. In this paper, we analyze the effect of antiviral therapy through mathematical modeling by using Liao’s homotopy analysis method (LHAM) that defines the connection between the target liver cells and the HBV. We also examine the basic nonlinear differential equation by LHAM to get a semi-analytical solution. This can be a very straight and direct method which provides the appropriate solution. Moreover, the local and global stability analysis of disease-free and endemic equilibrium is done using Lyapunov function. Mathematica 12 software is used to find out the solutions and graphical representations. We also discuss the numerical simulations up to sixth-order approximation and error analysis using the same software.

In this work, we discussed the solutions of viral dynamics in hepatitis B virus infection. Antiviral treatment for patients infected with hepatitis B virus is just somewhat proficient. The field is popular for understanding the associations between the virus, immune responses, short-term and long-term drug efficacy and the general strength of the liver. Furthermore, we investigated the Homotopy Perturbation Method (HPM) to construct the approximate analytical solution of the nonlinear differential equations arise in this model. Analytical results are compared with MATLAB simulation results and satisfactory agreement is noted.

This paper obtains a classical SEIR model of transmission dynamics and clinical dynamics in controlling of coronavirus disease 2019 (COVID-19) with Reproduction number. We discussed the parameter estimation of the transmission and clinical dynamics. The control of the COVID-19 was calculated by basic reproduction number. Therefore, the process was defined only epidemic calculator. The reproduction number value of above one or less than one are defined the recovery percentage of the whole mathematical modeling. The estimations of the basic reproduction number level may be as high as 10 (99.97% recuperated). Finally we illustrate the cure rate of the COVID-19 from the controlling of transmission dynamics parameters and also show the graphical representations from the numerical experiment.

A transmission dynamics of human SEIV-mosquitoes SEI model in malaria for deterministic compartmental model is discussed. We obtained to study its asymptotic criteria with equilibrium. We derive to find the global stability of disease free equilibrium and endemic equilibrium with compare the results from basic reproduction number is less than the unity.

We discuss the model for Swine flu transmission. We obtain to find the equilibrium points of the given swine flu model with the stability analysis and the endemic equilibrium is derived by Routh-Hurwitz conditions. Then, we calculate the disease free and endemic equilibrium for the numerical analysis with the help of MATLAB and to find the solutions of disease free equilibrium and endemic equilibrium. We compare this model results from the basic Ro for the numerical simulations of the seine flu model. These numerical simulations are used to verify our results.

In this proposed work we look at the analytical and numerical simulations of Dengue fever and recognize its best highlights alongside their execution for different situations. Dengue is a mosquito-borne viral disease. There are four particular, related, serotypes of the infection. Reviving from contamination by one gives long lasting invulnerability against that precise serotype. We are finding the solutions of nonlinear differential equations utilizing homotopy analysis method (HAM). We will utilize numerical simulations for MATLAB.

This paper deals the HBV infections using Homotopy Perturbation Method, Using Mathematical modeling for the three compartments such as T, I and V Where T denotes the target uninfected cells, I denotes infected cells, V denotes Hepatitis B virus in the dynamic models also Considering that β is the rate of target uninfected cells gets infected, and this happens when the target uninfected cells and virus interact with each other. Assuming that δ is the death rate of infected liver cells, and α is the production rate of virus. c is the death of virus. The new target cells are produced at the constant rate s and the target cells dies before getting infected at the rate dT and it’s the natural death, α, β , δ, c, s & d these six parameters estimations through the viral dynamics V, Homotopy Perturbation Method is used to derive the approximate solutions of the Nonlinear Differential Equation systems, The numerical solutions carried out from the MATLAB programme.

This paper deals with the higher-order principal component analysis of eigenvalues with special structures covariance matrices. The analysis obtained up to the higher order. The basic properties of three lemma’s are validating the problem. The principal components are derived from standard variables. Also, illustrate the principal elements for special structures covariance matrices.

We discussed the vector style delay of SI model with immigration. Thus, we have to obtain the unique solutions of Equilibrium of SI model with delay. Also, this paper we derive the solutions of local and global stability for asymptotically stable.We discussed the vector style delay of SI model with immigration. Thus, we have to obtain the unique solutions of Equilibrium of SI model with delay. Also, this paper we derive the solutions of local and global stability for asymptotically stable.

In this article, we have considered SEIR numerical model to depict the engendering of Influenza infection among population. Flu has been a consuming issue far and wide. Homotopy Perturbation Method (HPM) is executed to give analytical and estimated solutions of non linear ordinary differential equation systems of Influenza disease for SEIR Model.

The stability analysis of deterministic SEIA worm model in a computer network is considered. We calculate the disease free equilibrium and endemic equilibrium from the model. Here we have to find the numerical simulation compare with deterministic reproduction number. Also the numerical simulation of the anti-virus software failure rate constant obtain to derive the parameter estimation.

In this study, we have analyzed Hepatitis B virus to find out the analytical solutions for reducing the HBV infection. We also found the analytical solutions using Homotopy Perturbation Method (HPM) to find out the solution of nonlinear ordinary differential equation systems. SEICR models have been used to control the viral infections. Thus, we concentrated on examining the dynamics of Hepatitis B viral infection and how it must be controlled by vaccination and treatment method. The exactness and effectiveness of two methods has been analyzed by solvable ordinary differential equation systems. We mainly concentrated on steady controls for both vaccination and treatment. Finally, this paper depicts the analytical results which show that optimal combination of vaccination and treatment that will be the most useful way to control Hepatitis B virus infection.

The mathematical modeling of deterministic SEIA worm model in a computer network is considered. By constructing a suitable entire model, the schematic diagram of the full modeling and the non-linear system of this deterministic normalized model is investigated. He’s homotopy perturbation method (HPM) is applied to find the analytic solution of the system of nonlinear ordinary differential equations leading on the SEIA model

This paper deals with a mathematical model for Equine Infectious Anemia Virus (EIAV) infection with Cytotoxic T-lymphocyte (CTL) response delay proposed. Stability analysis of the disease-free steady-state and appropriate situations for local stability of immune-exhausted and infected steady-state is illustrated. Moreover, the existence of Hopf bifurcation is measured through concerning continuance lag such as a bifurcation parameter. Graphical replications are passed out toward elucidate our theoretical outcome. Keywords: EIAV infection, CTL, Hopf bifurcation

paper, we introduce delay differential equation (DDE) models of the hematopoietic system designed for the study of the effects of Granulocyte-Colony Stimulating Factor (G- CSF) administration. G-CSF is used clinically for treating subjects presenting low numbers of white blood cells, a condition referred to as Neutropenia that can result from different causes. The aim of this paper is to study alternative treatment that would minimize the use of G-CSF drug using a mathematical modeling. We propose is a parameter estimation model that considers G-CSF administration for Cyclical Neutropenia (CN), a dynamical disorder characterized by oscillations in the circulating neutrophil count. The model develops the dynamics of circulating blood cells before and after the G-CSF treatment. The model develops the equilibrium solution for the DDE and a sufficient condition for the global stability. The model focuses on the effects of two compartments forms of G-CSF for the treatment of CN (Fast Fourier Transform simulations). For each model, we use a combination of mathematical analysis and numerical simulations (linear chain trick) to study alternative G-CSF treatment that would be efficient while reducing the amount of drug. This reduces the quantity of G- CSF required for potential maintenance. This model gives us good result in treatment. The changes would be analytical and reduce the risk side as well as the cost of treatment in G-CSF.

We investigate the FFT (Fast Fourier Transform) model and G-CSF (granulocyte colony-stimulating factor) treatment of CN (Cyclical Neutropenia). We collect grey collies and normal dog’s data from CN and analyze the G-CSF treatment. The model develops the dynamics of circulating blood cells before and after the G-CSF treatment. This is quite natural and useful for the collection of laboratory data for investigation. The proposed interventions are practical. This reduces the quantity of G-CSF required for potential maintenance. This model gives us good result in treatment. The changes would be practical and reduce the risk side as well as the cost of treatment in G-CSF.

My idea of this paper is to discuss the MATLAB program for various mathematical modeling in ordinary differential equations (ODEs) and partial differential equations (PDEs). Idea of this paper is very useful to research scholars, faculty members and all other fields like engineering and biology. Also we get easily to find the numerical solutions from this program.

This paper is imposed an oscillatory behavior of nonlinear delay differential equation (NDDE). In particular, the main results got improve those studied in the literature survey. A variety of oscillatory behaviors are given.

The Pareto-Positive Stable(PPS) distribution is introduced as a new model for describing city size data of a region in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data and the classical Pareto and Zipf distributions are included as a particular case. The new distribution is compared with two classical models: Pareto and lognormal distribution. In all the data sets considered, the Newtons forward and backward(equal intervals), Lagrange interpolation formula(unequal interval) outperforms the fits of Pareto and lognormal distributions.