The paper considers the problem of least squares minimization with L-1-norm regularization functional. It investigates various smoothing approximations for the L-1-norm functional. It considers Quadratic, Sigmoid and Cubic Hermite functionals. A Tikhonov regularization is then applied to each of the resulting smooth least squares minimization problem. Results of numerical simulations for each smoothing approximation are presented. The results indicate that our regularization method is as good as any other non-smoothing method used in developed solvers.

Containment syringe sharing among individuals is considered to be the most contributing factor to human immunodeficiency virus (HIV). It’s well recognized that sharing syringes significantly contributes to the transmission of diseases amongst individuals. This study examines how syringe sharing may contribute to HIV infection and spread among injectable drug users. Sharing syringes greatly aids in the spread of infections among people, as is widely acknowledged. The model was calibrated using data from Malaysia from 2000 to 2011 on the incidence of HIV among drug injectors. Through the use of the Markov chain Monte Carlo simulation approach, the parameters are estimated using Bayesian inference. The basic reproduction number for HIV disease suggests that the disease-free equilibrium was stable during the 12 years. This is a good indicator from the public health point of view since the goal is to stabilize the infection rate. Our findings emphasized the potential involvement of syringe sharing in the transmission of HIV among injectable drug users and the need for more research into this infection rate in order to improve strategies for reducing the incidence of individual HIV cases among people who inject drugs.