Department of Mathematics

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Mathematics

This paper proposes and analyzes a nonlinear model for the biological control of algal bloom in a lake. Algal bloom often occurs in a lake due to excessive flow of nutrients from domestic drainage, industrial and agricultural waste, and this causes the decrease in the concentration of dissolved oxygen in the lake. Hence, it threatens the survival of other species of the ecosystem indirectly, and it is also responsible for the degradation of water quality in the lake because of less oxygen content. In this work we study biological control which means the introduction of predatory fish, i.e. the release of algae-eating fish into the lake to control the rapid growth of algae. We formulate our model by assuming Michaelis-Menten type ratio-dependent prey-predator interaction. The equilibrium of the mathematical model is found and also the stability is discussed in detail. It is observed that the positive equilibria is locally asymptotically stable under certain conditions on the parameters. Also the system is simulated for various sets of parameters and it is found that system may oscillate for some realistic set of parameters. In fact we found that the parameter m, which is the half saturation constant, is very sensitive and with the decrease in this parameter steady state solution of the system changes to stable oscillation. On the practical side, it means that the method of biological control by introducing predatory fish is not always beneficial because outcome of this method depends upon the actual value of the parameter. Here we get the paradox of biological control, which says that it is not possible to have low level of steady state equilibrium of prey population. © 2010 World Scientific Publishing Company.

School of Advanced Sciences

Chennai Campus

Journal of Biological Systems

Modeling biological control of algal bloom in a lake caused by discharge of nutrients

The main object of this paper is to prove several inclusion relations associated with the (n,δ) neighborhoods of various subclasses of convex functions of complex order by making use of the known concept of neighborhoods of analytic functions. © 2010 Austral Internet Publishing. All rights reserved.

World University root node

Australian Journal of Mathematical Analysis and Applications

Neighborhoods of certain subclasses of analytic functions of complex order with negative coefficients

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. © 2010 Elsevier Inc. All rights reserved.

Applied Mathematics and Computation

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

VIT Unitversity

Fulltext

African Journal of Biotechnology

Studies on the potency of oral polio vaccine using RD cell line and evaluation of growth using different serum concentration and volume of media

In this paper, a two-strain epidemic model with saturating contact rates is considered. It is shown that if the social activity of infected individuals does not vary with strains, then the competitive exclusion principle holds; if the social activity of infected individuals varies with different strains, the coexistence of pathogens is possible under a certain condition which involves the invasion reproduction numbers. The stability of the dominance equilibria and coexistence equilibrium is also examined. Numerical simulations are presented to illustrate the results. © 2008 Elsevier Ltd. All rights reserved.

Nonlinear Analysis: Real World Applications

Pathogen coexistence induced by saturating contact rates

A feedback arc set in a directed graph D is a set S of arcs in D such that D\S is acyclic. The problem of determining a feedback arc set with least number of arcs is NP - complete for a general digraph. We define the strong feedback arc number βs(G) for various orientations of an undirected graph G. The strong feedback arc problem of an undirected graph is to find a strong feedback arc set S of G(O) for some strongly oriented O(G) such that |S| = βs(G). In this paper our focus is on interconnection networks with βs = 1. © 2009 IEEE.

ICCTD 2009 - 2009 International Conference on Computer Technology and Development

Feedback arc set in oriented graphs

The paper investigates the global stability of a dengue epidemic model with saturation and bilinear incidence. The constant human recruitment rate and exponential natural death, as well as vector population with asymptotically constant population, are incorporated into the model. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. The stability of these two equilibria is controlled by the threshold number R0. It is shown that if R0 is less than one, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist; if R0 is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable. © 2009 Elsevier Ltd. All rights reserved.

Chaos, Solitons and Fractals

Global dynamics of a dengue epidemic mathematical model

Importance of estimating the centrality of the nodes in large networks has recently attracted increased interest. Betweenness is one of the most important centrality indices, which basically counts the number of shortest paths going through a node. Betweenness has been used in diverse applications such as social network analysis or route planning. In this paper we find a formula to obtain the betweeness-centrality for grids. © 2009 IEEE.

Betweeness-centrality of grid networks

An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. © 2009 Elsevier Ltd. All rights reserved.

Stability and bifurcation of an SIS epidemic model with treatment

In this paper, a stage-structured epidemic model with a nonlinear incidence with a factor Sp is investigated. By using limit theory of differential equations and Theorem of Busenberg and van den Driessche, global dynamics of the model is rigorously established. We prove that if the basic reproduction number R0 is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out; if R0 is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable. Numerical simulations support our analytical results and illustrate the effect of p on the dynamic behavior of the model. © 2009 Elsevier Inc. All rights reserved.