Analysis of a generalized model for influenza including differential susceptibility due to immunosuppression



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Recently, a mathematical model of pandemic influenza was proposed including typical control strategies such as antivirals, vaccination and school closure; and considering explicitly the effects of immunity acquired from the early outbreaks on the ulterior outbreaks of the disease. In such model the algebraic expression for the basic reproduction number (without control strategies) and the effective reproduction number (with control strategies) were derived and numerically estimated. A drawback of this model of pandemic influenza is that it ignores the effects of the differential susceptibility due to immunosuppression and the effects of the complexity of the actual contact networks between individuals. We have developed a generalized model which includes such effects of heterogeneity. Specifically we consider the influence of the air network connectivity in the spread of pandemic influenza and the influence of the immunosuppresion when the population is divided in two immune classes. We use an algebraic expression, namely the Tutte polynomial, to characterize the complexity of the contact network. Until now, The influence of the air network connectivity in the spread of pandemic influenza has been studied numerically, but not algebraic expressions have been used to summarize the level of network complexity. The generalized model proposed here includes the typical control strategies previously mentioned (antivirals, vaccination and school closure) combined with restrictions on travel. For the generalized model the corresponding reproduction numbers will be algebraically computed and the effect of the contact network will be established in terms of the Tutte polynomial of the network. © 2014 Copyright SPIE.


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