We propose a population model for HIV-TB co-infection dynamics by considering treatments for HIV infection, active tuberculosis and co-infection. The HIV only and TB only models are analyzed separately, as well as full model. The basic reproduction numbers for TB (R T 0 ) and HIV (R H 0 ) and overall reproduction number for the system R0 = max{R T 0 , R H 0 } are computed. The equilibria and their stability are studied. The main model undergoes supercritical transcritical bifurcation at R T 0 = 1 and R H 0 = 1 whereas the parameters β * = βe and λ * = λσ act as bifurcation parameters, respectively. Numerical simulation claims the existence of interior equilibrium when both the reproduction numbers are greater than unity. We explore the effect of early and late HIV treatment on disease-induced deaths during the TB treatment course. Mathematical analysis of our model shows that successful disease eradication requires treatment of single disease, that is, treatment for HIV only and TB only infected individuals with addition to co-infection treatment and in absence of which disease eradication is extremely difficult even for R0 < 1. When both the diseases are epidemic, the treatment for TB only infected individuals is very effective in reducing the total infected population and disease-induced deaths in comparison to the treatment for HIV infected individuals while these are minimum when both the single disease treatments are given with co-infection treatment.2010 Mathematics Subject Classification. Primary 92D30; Secondary 34C60, 34D20.

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Present day mobile robots are meant for very precise applications. For very precise applications of mobile robots, accurate estimation of inertial parameters depends upon the accuracy of mathematical model & as well as accuracy (error characteristics) of the individual sensor measurements. Sensor measurements are prone to various errors, which necessitates the detail modeling of sensors for estimation of useful signals from the noisy sensor measurements. Detail error modeling is essential to understand, identify & characterize the different types of noises present in the measured data using available mathematical techniques. This paper illustrates the frequency and time domain analysis techniques for characterization and identification of various noises present in the Laser Range Finder (Model: LMS200, SICK, Germany) measurements and their contribution to the overall noise statistics. A detailed methodology based on stochastic discrete time model is presented for Laser Range Finder error modeling.

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