Studying the efficacy of isolation as a control strategy and elimination of tuberculosis in India:A mathematical model

India has the highest burden of both tuberculosis(TB)and multidrug-resistant TB(MDRTB)based on the WHO Global TB Report 2019.Although the available data suggest that the total TB incidence has declined,the absolute number of new cases is still increasing.The number of reported TB cases in India in 2018 was 2.2 million,which was 1.5 million in 2009.About 47%increment in TB case notification in India within a decade shows a persistent public health problem.India contributes about 22%of the World's TB burden.Indian National Strategic Plan 2017e2025,sets out the government plans to eliminate TB by 2025.However,the milestone seems unrealistic to achieve the TB eradication goal by 2025.We developed a five-dimensional mathematical model to understand the TB dynamics in India and investigate the possibility of the earliest TB eradication time frame.The model stratifies the entire TB class into three different classes as drug-sensitive(DS),MDR,and isolated classes.The effective reproduction number,equilibrium points,and stability analysis of the model were carried out.This model predicts the total estimated cases of DS-TB and MDR-TB from 2018 to 2035 through numerical simulation and suggests that TB may be eliminated by 2035 in India if the treatment success rate could be achieved to 95%,by contact tracing and isolating at least 50%of MDR-TB.

Fractal dynamics and computational analysis of local fractional Poisson equations arising in electrostatics

In this paper,the local fractional natural decomposition method(LFNDM)is used for solving a local fractional Poisson equation.The local fractional Poisson equation plays a significant role in the study of a potential field due to a fixed electric charge or mass density distribution.Numerical examples with computer simulations are presented in this paper.The obtained results show that LFNDM is effective and convenient for application.

Approximate analytical solution of fractional order biochemical reaction model and its stability analysis

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.