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

100%

Saha S. , Roy P. K.

tom Vol. 27, no. 2

337--350

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.

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

100%

Datta A. , Roy P. K.

tom Vol. 42, no. 2

365--386

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.

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

80%

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

2017

tom Vol. 46, no. 4

325--344

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.