Joydip Dhar, Mani Tyagi, P. Sinha
ABV-Indian Institute of Information Technology and Management
Gwalior (M.P.), INDIA
Department of Mathematics
Govt. Model Science College
Gwalior, 474015 (M.P.), INDIA

Abstract. In this paper, we propose a compartmental model to study the influence of word of-mouth to the spreading of information of new product with the market dynamics with two competitive products in a given closed region. The model was analyzed qualitatively to determine the possible steady states and it's local stability under the influence of personal interaction. Here, we calculated the basic influence numbers(BINs) for both the products and combined BIN of the proposed system. It is observed that adopter free equilibrium is locally stable only when the BINs are less than one for both the product and interior equilibrium is always unstable, hence in long run the co-existence of both the product is the market is impossible. Further, it is also shown that value of BINs will determine the survival of a particular product. Finally, numerical justification of the analytical results are performed with different set of values and presented graphically in the numerical section.

Received: March 13, 2013

AMS Subject Classification: 91FXX, 34CXX, 34DXX

Key Words and Phrases: innovation diffusion, compartment model, basic influence number, local stability

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