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.