A Hybrid Identification Method for Mathematical Models for Zika Virus

ABSTRACT This paper studies some deterministic mathematical models that seek to explain the expansion of Zika virus, as a viral epidemic, using published data for Brazil. Three SIR type models considering several aspects in the spread of the disease are considered with 3, 6, and 10 unknown parameters, respectively. The parameter identification is carried through a search algorithm based on a combination of a stochastic domain exploration and a heuristic calculation of a descent direction, in order to avoid stopping the algorithm at a local optimum. The models are validated using the epidemic data found. Finally, it was confirmed that the basic reproductive ratio is consistent with those previously reported in the literature. We conclude that the proposed optimization method improves computation time with respect to a genetic algorithm or an exhaustive search in the parameter space.