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An Agent-Based Model with Drift and Cross-Immunity for Influenza

An agent-based model is used to describe the dynamics of influenza drift and cross-immunity in host populations with different characteristics. Each different mutation of the virus is represented as a point in a two-dimensional space, constructed in such a way to represent the genetic distances between the mutations (genetic map). A strain of the virus is represented by a region in that map. Each individual has a history of all his previous infections, represented by a vector consisting of points in the map. At a given time each infected individual will have contact with other individuals of the population. The probability that this contact results in an infection depends on how far the virus is from the closest point in the history of the individual to be infected (cross-immunity). If contact is effective, the individual will be infected in the next time period. However, since the virus may mutate in the host in the next time period, the active mutation generated will differ from the one that caused the initial infection; but will remain genetically close to it (drift). This work was motivated and gives special attention to the infection of influenza in the tropics, since this area has not been well characterized by mathematical models. Patterns similar to the ones observed in the tropics are obtained in the simulations with low values of infection probability or contact rate.

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Jorge A. Alfaro-Murillo, Purdue University