Community-based Immunization Strategies for Epidemic Control

Understanding the epidemic dynamics, and finding out efficient techniques to control it, is a challenging issue. A lot of research has been done on targeted immunization strategies, exploiting various global network topological properties. However, in practice, information about the global structure of the contact network may not be available. Therefore, immunization strategies that can deal with a limited knowledge of the network structure are required. In this paper, we propose targeted immunization strategies that require information only at the community level. Results of our investigations on the SIR epidemiological model, using a realistic synthetic benchmark with controlled community structure, show that the community structure plays an important role in the epidemic dynamics. An extensive comparative evaluation demonstrates that the proposed strategies are as efficient as the most influential global centrality based immunization strategies, despite the fact that they use a limited amount of information. Furthermore, they outperform alternative local strategies, which are agnostic about the network structure, and make decisions based on random walks.Comment: 6 pages, 7 figure

Centrality Measures for Networks with Community Structure

Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order to find the influential nodes, while on the other end, random strategies are completely agnostic about the network structure. Centrality measures that can deal with a limited knowledge of the network structure are required. Indeed, in practice, information about the global structure of the overall network is rarely available or hard to acquire. Even if available, the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures. To that end, a centrality measure is proposed that requires information only at the community level to identify the influential nodes in the network. Indeed, most of the real-world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes. We performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies with an available and the proposed deterministic community-based strategy. Effectiveness of the proposed method is evaluated by performing experiments on synthetic and real-world networks with community structure in the case of immunization of nodes for epidemic control.Comment: 30 pages, 4 figures. Accepted for publication in Physica A. arXiv admin note: text overlap with arXiv:1411.627

(R1971) Analysis of Feedback Queueing Model with Differentiated Vacations under Classical Retrial Policy

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical interpretation of the results obtained. Finally, the cost is optimized using the parabolic method

DESIGNING AND OPTIMIZATION OF NAPROXEN SODIUM DEFORMABLE VESICULAR SYSTEMS THROUGH FACTORIAL DESIGN: BOX BEHENKEN MODEL

Objective: The objective of this investigation was to develop and statistically optimize deformable vesicles such as transfersomes and transethosomes of Naproxen sodium by employing 33factorial designs through software Design expert version 12 (Box–Behnken design) for dermal delivery. Methods: The levels of the drug, phosphatidylcholine, and span 80 (independent variables) were varied to study the influence on vesicle size and % entrapment efficiency (dependent variables) of transfersomes and for transethosomes, the levels of phosphatidylcholine, ethanol, and span 80 were selected as independent variables Second-order quadratic polynomial equation, 2D and 3D contour plots represented the relationship between variables and desired response. The optimization process was carried out using desirability plots and point prediction techniques. Results: Results of the present study demonstrated that optimized transfersomes and transethosomes showed vesicle sizes of 114.91 nm and 102.91 nm respectively, while entrapment efficiency of 80.11 % and 86.97%, respectively. Both formulations showed high zeta potential values indicating the stability of the optimized formulation. ANOVA statistical results showed a significant difference (P<0.05). Conclusion: The results indicated that the independent variable plays a crucial role in optimizing a formulation that can be used for further research studies. Present preliminary study data provided strong evidence that the optimized deformable vesicular formulations through box Behnken factorial design can be a potentially useful drug carrier for naproxen sodium dermal delivery with minimum vesicle size and efficient entrapment efficiency

A note on squeezing function and its generalizations

This note investigates the relation between squeezing function and its generalizations. Using the relation obtained, we present an alternate method to find expression of generalized squeezing function of unit ball corresponding to the generalized complex ellipsoids.Comment: 9 page

Squeezing function corresponding to polydisk

In the present article, we define squeezing function corresponding to polydisk and study its properties. We investigate relationship between squeezing fuction and squeezing function corresponding to polydisk.Comment: Published in Complex Analysis and its Synergie