Qualitative behavior of SIS epidemic model on time scales
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
Pair approximations for ecological models with additional neighborhood effects
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
Effect of incubation period of virus for the mathematical model of dengue disease
CONTROL'07 Proceedings of the 3rd WSEAS/IASME international conference on Dynamical systems and control
Transmission model for Plasmodium vivax malaria
CONTROL'07 Proceedings of the 3rd WSEAS/IASME international conference on Dynamical systems and control
Immunization strategies for networks with scale-free topology
NOLASC'06 Proceedings of the 5th WSEAS international conference on Non-linear analysis, non-linear systems and chaos
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A mathematical model using either mean-field approximation or pair approximation has both advantage and limitation. Mean-field approximation is suitable for describing behaviors of a large system; however, it neglects the scale of individual interaction. On the other hand, pair approximation is suitable for studying local interaction especially singles and pairs; however, the mathematical formulas are still limited. Thus, choosing the right model for the right purpose is recommended. The objective of this paper is to develop the techniques of pair approximation by using probability averaged value based on probability distribution; for example, multinomial distribution and Poisson distribution. These extended formulas are suitable for a model composed of individuals whose event rates are additionally affected by their nearby neighbor. Finally, we apply these tools to a simple SIS epidemic model.