Md. Haider Ali Biswas

A variant of nonsmooth maximum principle for state constrained problems

We derive a variant of the nonsmooth maximum principle for problems with pure state constraints. The interest of our result resides on the nonsmoothness itself since, when applied to smooth problems, it coincides with known results. Remarkably, in the normal form, our result has the special feature of being a sufficient optimality condition for linear-convex problems, a feature that the classical Pontryagin maximum principle had whereas the nonsmooth version had not. This work is distinct to previous work in the literature since, for state constrained problems, we add the Weierstrass conditions to adjoint inclusions using the joint subdifferentials with respect to the state and the control. Our proofs use old techniques developed in [16], while appealing to new results in [7].

Nonlinear Dynamical Systems in Modeling and Control of Infectious Disease

This paper deals with nonlinear dynamical systems in the form of mathematical modeling to describe modeling of the dynamic behavior of biological and biomedical systems. Nonlinear ordinary differential equations have been studied to investigate the mysterious and complex mechanisms of the dynamics of infectious diseases in the human body. In particular, we study a nonlinear model of HIV immunology which describes the interactions between the human immune systems and the viruses. In this work, we propose a modification of the HIV model proposed by Joshi in Optim Control Appl Methods 23(4):199–213 (2002) by introducing state constraint to the dynamics. The aim is to obtain optimal immunotherapeutic strategy where the state constraint may play a crucial role. We treat our problem numerically and compare the results with existing literature to illustrate the significant effect of introducing state constraint to the dynamics of the model.

A mathematical analysis for controlling the spread of Nipah virus infection

Abstract Nipah virus (NiV) infection is actually a panicky fright in the South-East Asian regions. Though this emerging infectious disease is one of the most alarming threats of the public health in these regions, the treatment of this disease is limited. In this study, we propound and analyze a mathematical model for controlling the spread of NiV infection with vital dynamics (birth and death rates are not equal), incorporating the quarantines of infectious individuals influenced by availability of isolation centers and surveillance coverage. What is more, we take into account on improved personal hygiene of the susceptible population influenced by public enlightenment campaign. It has been showed with the numerical simulations that improved personal hygiene and quarantining of infectious individuals are enough to control the spread of NiV and with improved personal hygiene, it will be more effective and efficient of the two control parameters.

A mathematical model for understanding the spread of nipah fever epidemic in Bangladesh

In this paper, a mathematical model for the nipah virus (NiV) infections, commonly known as “nipah fever” in Bangladesh is proposed. The host-pathogen interaction of NiV infection in terms of nonlinear ordinary differential equations (ODEs) is studied. The aim is to investigate the disease propagation and control strategy of NiV infections. The behavior of the dynamics of NiV infections as well as the optimal control strategy has been studied in vein of optimal control theory and the results are presented with an illustration by the numerical simulations.