Periodic Orbits in the Photogravitational Restricted Problem When the Primaries Are Triaxial Rigid Bodies

We have studied periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are triaxial rigid bodies and source of radiation pressure. We have determined periodic orbits for different values of (h is energy constant;μ is mass ratio of the two primaries;are parameters of triaxial rigid bodies and are radiation parameters). These orbits have been determined by giving displacements along the tangent and normal at the mobile co-ordinates as defined in our papers (Mittal et al. [1]-[3]). These orbits have been drawn by using the predictor-corrector method. We have also studied the effect of triaxial bodies and source of radiation pressure on the periodic orbits by taking fixed value of μ.

Effect of Perturbations in Coriolis and Centrifugal Forces on the Non-Linear Stability of <i>L</i>₄in the Photogravitational Restricted Three Body Problem

Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.

Restricted Three Body Problem with Stokes Drag Effect

The existence and stability of stationary solutions of the restricted three body problem under the effect of the dissipative force, Stokes drag, are investigated. It is observed that there exist two non collinear stationary solutions. Further, it is also found that these stationary solutions are unstable for all values of the parameters.

Estimating the impact of antiretroviral therapy on HIV-TB co-infection:Optimal strategy prediction

In this paper,a nonlinear population model for HIV-TB co-infection has been proposed.The model is incorporated with the effect of early and late initiation of HIV treatment in co-infectives already on TB treatment,on the occurrence of Immune Reconstitution Inflammatory syndrome(IRIS).A 15-dimensional(15D)mathematical model has been developed in this study.We begin with considering constant treatment rates and thereafter,proceed to time-dependent treatment rates for co-infectives as control parameters.The basic reproduction number,a threshold quantity,corresponding to each HIV and TB sub-model has been computed in case of constant controls.With constant values of control parameters,mathematical analysis shows the existence and local stability of the disease-free equilibrium point and the endemic equilibrium point for the model.Together with time-dependent parameters,an optimal control problem is introduced and solved using Pontryagin’s maximum principle with an objective to minimize the number of infectives and disease induced deaths along with the cost of treatment.Numerical simulations are performed to examine the effect of reproduction numbers on control profiles and to identify,the ideal combination of treatment strategies which provides minimum burden on a society.Numerical results imply that if both HIV and TB are endemic in the population,then in order to bring in minimum burden from the co-infection,optimal control efforts must be enforced rather than constant treatment rate.

Assessing the impact of transmissibility on a cluster-based COVID-19 model in India

In this paper,we have proposed a nonlinear mathematical model of different classes of individuals for coronavirus(COVID-19).The model incorporates the effect of transmission and treatment on the occurrence of new infections.For the model,the basic reproduction number(R_(0))has been computed.Corresponding to the threshold quantity(R_(0)),the stability of endemic and disease-free equilibrium(DFE)points are determined.For R_(0)>1,if the endemic equilibrium point exists,then it is locally asymptotically stable,whereas the DFE point is globally asymptotically stable for R_(0)<1 which implies the eradication of the disease.The effects of various parameters on the spread of COVID-19 are discussed in the segment of sensitivity analysis.The model is numerically simulated to understand the effect of reproduction number on the transmission dynamics of the disease COVID-19.From the numerical simulations,it is concluded that if the reproduction number for the coronavirus disease is reduced below unity by decreasing the transmission rate and detecting more number of infectives,then the epidemic can be eradicated from the population.