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.

Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model.

To understand dynamics of the COVID-19 disease realistically, a new SEIAPHR model has been proposed in this article where the infectious individuals have been categorized as symptomatic, asymptomatic, and super-spreaders. The model has been investigated for existence of a unique solution. To measure the contagiousness of COVID-19, reproduction number R 0 is also computed using next generation matrix method. It is shown that the model is locally stable at disease-free equilibrium point when R 0 < 1 and unstable for R 0 > 1 . The model has been analyzed for global stability at both of the disease-free and endemic equilibrium points. Sensitivity analysis is also included to examine the effect of parameters of the model on reproduction number R 0 . A couple of optimal control problems have been designed to study the effect of control strategies for disease control and eradication from the society. Numerical results show that the adopted control approaches are much effective in reducing new infections.

On implementation of a semi-analytic strategy to develop an analytical solution of a steady-state isothermal tube drawing model.

In this paper, we consider an isothermal glass tube drawing model consisting of three coupled nonlinear partial differential equations. The steady-state solution of this model is required in order to investigate its stability. With the given initial and boundary conditions, it is not possible to determine an analytical solution of this model. The difficulty lies in determining the constants of integrations while solving the second order ordinary differential equation analytically appearing in the steady-state model. To overcome this difficulty, we present a numerical based approach for the first time to develop an analytical solution of the steady-state isothermal tube drawing model. We use a numerical technique called shooting method to convert the boundary value problem into a set of initial value problems. Once the model has been converted into a system of differential equations with initial values, an integrating technique is implemented to develop the analytical solution. The computed analytical solution is then compared with the numerical solution to better understand the accuracy of obtained solution with necessary discussions.