Wyniki wyszukiwania - BazTech

1

A comparative study between two systems with and without awareness in controlling HIV/AIDS

Saha S., Roy P. K.

International Journal of Applied Mathematics and Computer Science

|

2017

|

Vol. 27, no. 2

337--350

EN

It has always been a priority for all nations to reduce new HIV infections by implementing a comprehensive HIV prevention programme at a sufficient scale. Recently, the ‘HIV counselling & testing’ (HCT) campaign is gaining public attention, where HIV patients are identified through screening and immediately sent under a course of antiretroviral treatment (ART), neglecting the time extent they have been infected. In this article, we study a nonlinear mathematical model for the transmission dynamics of HIV/AIDS system receiving drug treatment along with effective awareness programs through media. Here, we consider two different circumstances: when treatment is only effective and when both treatment and awareness are included. The model is analyzed qualitatively using the stability theory of differential equations. The global stabilities of the equilibria under certain conditions are determined in terms of the model reproduction number. The effects of changes in some key epidemiological parameters are investigated. Projections are made to predict the long term dynamics of the disease. The epidemiological implications of such projections on public health planning and management are discussed. These studies show that the aware populations were less vulnerable to HIV infection than the unaware population.

2

Impact of roguing and insecticide spraying on mosaic disease in Jatropha curcas

Al-Basir F., Roy P. K., Ray S.

Control and Cybernetics

|

2017

|

Vol. 46, no. 4

325--344

EN

Jatropha curcas plant is greatly impaired by mosaic disease, caused by the viruses (Begomovirus), transmitted by whiteﬂies, which act as the vector. Roguing (i.e. removal of infected plant) and spraying of insecticides are common methods, employed in order to get rid of the disease. In this article, a mathematical model has been developed to study the mosaic disease dynamics while considering preventive measures of roguing and insecticide spraying. Suﬃcient conditions for the stability of equilibrium points of the system are among the results obtained through qualitative analysis. We obtain the basic reproduction number R0 and show that the disease free system is stable for R0 < 1 and unstable for R0 > 1. The region of stability of equilibrium points in diﬀerent parameter spaces have also been analysed. Hopf bifurcation at the endemic steady state has been studied subsequently, as well. Finally, by formulating an optimal control problem, optimal application of roguing and spraying techniques has been determined, keeping in mind the cost eﬀective control of the mosaic disease. Pontryagin minimum principle has been utilized to solve the optimal control problem. Numerical simulations illustrate the validity of the analytical outcomes.

3

Optimal control of a fractional-order enzyme kinetic model

Al-Basir F., Elaiw A. M., Kesh D., Roy P. K.

Control and Cybernetics

|

2015

|

Vol. 44, no. 4

443--461

EN

Enzymes play a signiﬁcant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.

4

T-cell proliferation on immunopathogenic mechanism of psoriasis: a control based theoretical approach

Datta A., Roy P. K.

Control and Cybernetics

|

2013

|

Vol. 42, no. 2

365--386

EN

Psoriasis vulgaris is a common, worldwide autoimmune skin disorder characterized by T-cells mediated hyperproliferation of keratinocytes. The feature of T-cells arbitrated psoriatic lesions is the epidermal infiltration of oligoclonal CD8+ T-cells and also of CD4+ T-cells in the dermis. Psoriatic scratches are identified by red and enlarged lesions along with silver whitish scales. In this article, we propose a mathematical model for psoriasis, involving a set of differential equations, concerning T-cells, dendritic cells and epidermal keratinocytes. We introduce T-cell proliferation in the system, where T-cells are generated through expansion of accessible CD4+ T-cells from precursors. We are interested in observing how the cell biological system develops through T-cell proliferation in presence of control with respect to T-cells and keratinocytes. We study the model in both implicit and explicit ways and measure the effect of drug on the system through impulsive drug therapy.

5

Mathematical modeling to optimize the product in enzyme kinetics

Nandi S., Ghosh M. K., Bhattacharya R., Roy P. K.

Control and Cybernetics

|

2013

|

Vol. 42, no. 2

431--442

EN

Optimization of product in enzyme kinetics is successful by the showers of mathematical analysis with control measures. Enzymes are an important functional aspects of all biochemical processes, as they catalyze numerous reaction taking place within living organisms. With this view, optimization and quantification of product is stressed upon and in such a context, optimal control approaches have been applied in our study. In this article, we have formulated a mathematical model of enzymatic system Dynamics with control measures with a view to optimize the product as well as process conditions. Here, Pontryagin Minimum Principle is used for determination of optimal control with the help of Hamiltonian. We discuss the relevant numerical solutions for the concentration of substrate, enzyme, complex and product with respect to a specified time interval by varying control factors.