A mathematical model for Dengue and Chikungunya in Mexico.

We present a model that incorporates two co-circulating viral diseases, Dengue and Chikungunya, where we allow secondary infections from either of the two diseases. We only consider one vector population, Ae. aegypti since in the Mexican region where we set our scenarios, only this species has been reported to transmit both viruses. We estimate the basic reproduction number and perform numerical simulations for different scenarios where we may observe coexistence of Dengue and Chikungunya; we also compare the results of the model with Dengue and Chikungunya data from Mexico 2015 and we obtain a good model fit. To complete our findings we perform a sensitivity analysis, and calculate the partial rank correlation coefficients (PRCCs) to determine the parameter values influence on the reproduction numbers and predict fate of the diseases. We show that R0 for each one of the viruses is highly sensitive to the mosquito biting rate and the transmission rates for both diseases with positive ifluence and the average lifespan of mosquito along with the human recovery rate with negative ifluence on both diseases. Our results are consistent with those of previous authors.