Mathematical Modeling of Influenza Subtypes

This book is concerned with mathematical modeling and optimal control of influenza A subtypes H1N1 and H5N1. Mathematical models are derived to better understand the transmission and spread of the diseases, and then the dynamical behavior with all possible equilibria of the proposed model for influenza are also discussed. The backward bifurcation phenomenon suggests that the reproductive number R0 < 1 is not enough to eliminate influenza H1N1 from the population under consideration. So an accurate estimation of parameters and level of control measures are important to reduce the spread of influenza in an endemic region. To prevent the future pandemic of emerging avian-influenza H5N1, a human-to-human transmittable compartmental model is proposed. By using optimal control theory, the proposed models to assess the impact of some control measures is extended. The proposed control techniques for the elimination of influenza H1N1 mainly depend on vaccination coverage but since the vaccine for avian-influenza is not available in the market yet, therefore the emphasize is on education campaign and isolation of the infectious individuals.