Chikungunya is a vector-borne viral disease caused by the mosquitoes Aedes aegypti and Aedes albopictus. There is no specific medical treatment or available vaccine. This work presents a host-vector model that considers two age structures: chronological age and asymptomatic infection age. This model accounts for variability in the relapse period and susceptibility to the chikungunya virus. From this system of integro-differential equations, a particular case is derived in the form of ordinary differential equations (ODEs). The objective of this study is to estimate the basic reproductive number R0 of the ODE model for a chikungunya outbreak that occurred in 2015 in Acapulco, Mexico. A Bayesian approach using Hamiltonian Monte Carlo methods is applied to estimate the parameters of the ODE model and subsequently estimate R0. We estimate that R0 is 2.61, with a 95% credibility interval of (1.66, 3.80), which is consistent with other reports in the literature.