Computational analysis of control of hepatitis B virus disease through vaccination and treatment strategies.

Hepatitis B disease is an infection caused by a virus that severely damages the liver. The disease can be both acute and chronic. In this article, we design a new nonlinear SVEICHR model to study dynamics of Hepatitis B Virus (HBV) disease. The aim is to carry out a comprehensive mathematical and computational analysis by exploiting preventive measures of vaccination and hospitalization for disease control. Mathematical properties of proposed model such as boundedness, positivity, and existence and uniqueness of the solutions are proved. We also determine the disease free and endemic equilibrium points. To analyze dynamics of HBV disease, we compute a biologically important quantity known as the reproduction number R0 by using next generation method. We also investigate the stability at both of the equilibrium points. To control the spread of disease due to HBV, two feasible optimal control strategies with three different cases are presented. For this, optimal control problem is constructed and Pontryagin maximum principle is applied with a goal to put down the disease in the population. At the end, we present and discuss effective solutions obtained through a MATLAB code.

New series of 3,5-disubstituted tetrahydro-2H-1,3,5-thiadiazine thione (THTT) derivatives: Synthesis and potent antileishmanial activity.

Four series of heterocyclic compounds, namely, tetrahydro-2H-1,3,5-thiadiazine thione derivatives were synthesized in good to excellent yields and were screened for their in vitro antileishmanial activities against Leishmania major (promastigotes). Most of the compounds showed significant antileishmanial activity within the range of IC50 = 15.48-39.36 µM when compared with standard pentamidine (IC50 = 14.95 µM). The structure-activity relationship showed that N-3 and N-5 substituents have a key role against leishmanicidal activity. The ester analogues (series B) were found to have a 1.5 to 5-fold reduced activity compared to their acidic counterparts. Cytotoxicity against mammalian mouse fibroblast 3 T3 cells was also evaluated and compared between the acid and its ester analogue. The reduction of antileishmanial activity and loss of toxicity in the newly developed THTT ester derivative indicates that these compounds can be used as a template study for the production of effective antileishmanial ester prodrugs.