Priti Kumar Roy

Entropy based region reducing genetic algorithm for reliability redundancy allocation in interval environment

Abstract This research paper presents a multi-objective reliability redundancy allocation problem for optimum system reliability and system cost with limitation on entropy of the system which is very essential for effective sustainability. Both crisp and interval-valued system parameters are considered for better realization of the model in more realistic sense. We propose that the system cost of the redundancy allocation problem depends on reliability of the components. A subpopulation and entropy based region reducing genetic algorithm (GA) with Laplace crossover and power mutation is proposed to determine the optimum number of redundant components at each stage of the system. The approach is demonstrated through the case study of a break lining manufacturing plant. A comprehensive study is conducted for comparing the performance of the proposed GA with the single-population based standard GA by evaluating the optimum system reliability and system cost with the optimum number of redundant components. Set of numerical examples are provided to illustrate the effectiveness of the redundancy allocation model based on the proposed optimization technique. We present a brief discussion on change of the system using graphical phenomenon due to the changes of parameters of the system. Comparative performance studies of the proposed GA with the standard GA demonstrate that the proposed GA is promising to solve the reliability redundancy optimization problem providing better optimum system reliability.

Effect of HAART on CTL Mediated Immune Cells: An Optimal Control Theoretic Approach

Highly active antiretroviral therapy (HAART) reduces the virus load during long term drug therapy. It is observed that during drug therapy virus load sustained in the immune system also CTL is generated due to activation of immune cells and declination of memory CTL which is actually the causal effect of suppression of virus load. Here we extended our work (Roy PK, Chatterjee AN (2010) Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010, pp 615–620) and formulate a set of differential equations to study the effect of HAART on immune cells to a HIV infected individuals. We also incorporate in our model of an optimal control strategy during drug treatment, which reduces the infected cell population and increases the uninfected cell population. It is to be mentioned here that the control variable is used as drug dose which introduces in the diseases transmission term. Analytical and numerical study shows that optimal control process can reduces the infected cell population. An objective function is also introduced to minimize the systemic cost of chemotherapy.

Anti-viral drug treatment along with immune activator IL-2: a control-based mathematical approach for HIV infection

Recent development in antiretroviral treatment against HIV can help AIDS patients to fight against HIV. But the question that whether the disease is to be partially or totally eradicated from HIV infected individuals still remains unsolved. Usually, the most effective treatment for the disease is HAART which can only control the disease progression. But as the immune system becomes weak, the patients can not fight against other diseases. Immune cells are activated and proliferated by IL-2 after the identification of antigen. IL-2 production is impaired in HIV positive patients and intermitted administration of immune activator IL-2 together with HAART which is a more effective treatment to fight against the disease. Thus, its expediency is essential and is yet to be explored. In this article we anticipated a mathematical model of the effect of IL-2 together with RTIs therapy in HIV positive patients. Our analytical as well as numerical study shows that the optimal schedule of treatment for best result is to be obtained by systematic drug therapy. But at the last stage of treatment, the infection level raises again due to minimisation of drug dosage. Thus we study the perfect adherence of the drugs and found out if RTIs are taken with sufficient interval then for fixed interval of IL-2 therapy, certain amount of drug dosages may be able to sustain the immune system at pre-infection stage and the infected CD4+T cells are going towards extinction.

A MATHEMATICAL MODEL ON CTL MEDIATED CONTROL OF HIV INFECTION IN A LONG-TERM DRUG THERAPY

Bonhoeffer et al.1 studied the long-term dynamics of HIV drug therapy and virus load dynamics. It is well known that highly active anti retroviral therapy (HAART) can effectively control the HIV replication. It is also well known that reverse transcriptase inhibitors (RTIs) could block new infection and as a result control HIV infection. The positive feedback control on such dynamics plays an important role and CD4+T cells are not only produced from a source but also produced from existing T cells. The present investigation takes into account these factors in the original model of Bonhoeffer et al. The optimal control therapy and the effect of time delay in the positive feedback control function have been investigated. Numerical simulation of the nonlinear model has confirmed our analytical studies.

Mathematical Modelling of Enfuvirtide and Protease Inhibitors as Combination Therapy for HIV

Abstract Enfuvirtide (formerly T20) is an injectable fusion inhibitor that has established effective antiretroviral activity and excellent tolerability in extensively pretreated patients. This fusion inhibitor does not affect the metabolism of other co-administrated drugs for metabolic drug interactions involving enfuvirtide. Few mathematical models have considered co-administration of antiretroviral drugs. We develop a mathematical model to study the effect of enfuvirtide upon this process in combination with protease inhibitors (PIs) using impulsive differential equations. We divide the T cells into several classes to describe the drug activity. Analytical results show that a combination of enfuvirtide and PIs gives a better outcome than single drug activity; furthermore, use of enfuvirtide clearly outranks PIs if only one class of drugs were to be used. We determine the threshold value for the dosage and dosing intervals to ensure the stability of the disease-free state and illustrate our results with numerical simulations. We recommend that use of enfuvirtide, in combination with PIs, be expanded beyond salvage therapy.

A Mathematical Approach to Control Cutaneous Leishmaniasis Through Insecticide Spraying

Leishmaniasis is one sort of the vector born diseases, which is transmitted to human or animals by sand-fly bites. Single cell parasite grounds skin infection called Cutaneous Leishmaniasis. In our current research article, we consider a simple mathematical model to analyze the disease dynamics of Cutaneous Leishmaniasis consisting susceptible and infected populations of human and vector. In this article, our focus is to reduce the vector population so that the disease may be controlled. Here we try to explore the effect of insecticide for controlling the vector population through impulsive mode. We have established the efficiency of the insecticide spraying, which contributes a greater impact on the dynamics to move the system towards disease free situation.

Modeling of a control induced system for product formation in enzyme kinetics

Double substrate enzyme kinetics has a leading role for product quantification and optimization in different chemical and biochemical sectors. Mathematical approach for controlling these reactions in different stages by suitable parameters adds a new dimension in this interdisciplinary field of research. Applying control theoretic approach in the reversible backward stages of double substrate enzymatic model, time economization with regard to product formation is significant. In this article, we formulate a double substrate mathematical model of enzymatic dynamical reaction system with control measures with a view to observe the effect of changes of these measures with respect to the concentration of substrates, enzyme, complexes and finally product. Here, Pontryagin Minimum Principle is used for observing the effect of control measures in the system dynamics with the help of Hamiltonian. We compare the relevant numerical solutions for the substrates, enzyme, complexes and product concentration profile for a specified time interval with respect to control factors.

Virus replication factor may be a controlling agent for obtaining disease-free system in a multi-species eco-epidemiological system

The role of viruses in marine phytoplankton-zooplankton community structure is undoubtedly very important. In this paper, we propose a simple mathematical model for phytoplankton-zooplankton (prey-predator) system with an additional factor that the viral disease is spreading only among the prey species. Considering high abundance and importance of viruses in aquatic environments we have explicitly considered here the growth equation of free viruses and have studied this four-dimensional model analytically. It is observed that the disease-free system can be obtained when the virus replication factor lies in-between certain critical values. Numerical simulations have also been performed to substantiate the analytical findings.

Fractional-order model of the disease Psoriasis: A control based mathematical approach

Autoimmune diseases are generated through irregular immune response of the human body. Psoriasis is one type of autoimmune chronic skin diseases that is differentiated by T-Cells mediated hyper-proliferation of epidermal Keratinocytes. Dendritic Cells and CD8+ T-Cells have a significant role for the occurrence of this disease. In this paper, the authors have developed a mathematical model of Psoriasis involving CD4+ T-Cells, Dendritic Cells, CD8+ T-Cells and Keratinocyte cell populations using the fractional differential equations with the effect of Cytokine release to observe the impact of memory on the cell-biological system. Using fractional calculus, the authors try to explore the suppressed memory, associated with the cell-biological system and to locate the position of Keratinocyte cell population as fractional derivative possess non-local property. Thus, the dynamics of Psoriasis can be predicted in a better way using fractional differential equations rather than its corresponding integer order model. Finally, the authors introduce drug into the system to obstruct the interaction between CD4+ T-Cells and Keratinocytes to restrict the disease Psoriasis. The authors derive the Euler-Lagrange conditions for the optimality of the drug induced system. Numerical simulations are made through Matlab by developing iterative schemes.

Network reliability evaluation for fuzzy components: An interval programming approach

The probabilistic reliability estimation of complex system is complicated due to uncertainty of failure data, modeling or human failure. In this paper, reliability of components of complex network system is considered as fuzzy in nature to reduce the uncertainty. Trapezoidal fuzzy number is used to represent component’s reliability of network system. Then the reliability of the network system is assembled with fuzzy reliability of components and evaluated by Zadeh’s extension principle. Fuzzy reliability of the network system becomes an interval by -cuts operation. Interval nonlinear programming is used to evaluate the optimum network’s system reliability with interval valued cost constraint. The above approach is explained in details through a numerical example of very useful power system network of electrical engineering.