Human metapneumovirus (HMPV) have similar symptoms to those caused by respiratory syncytial virus (RSV). The modes of transmission and dynamics of these epidemics still remain poorly understood. Climatic factors have long been suspected to be implicated in impacting on the number of cases for these epidemics. Currently, only a few models satisfactorily capture the dynamics of time series data of these two viruses. In this study, we used a negative binomial model to investigate the relationship between RSV and HMPV while adjusting for climatic factors. We specifically aimed at establishing the heterogeneity in the autoregressive effect to account for the influence between these viruses. Our findings showed that RSV contributed to the severity of HMPV. This was achieved through comparison of models of various structures, including those with and without interaction between climatic cofactors. The study has improved our understanding of the dynamics of RSV and HMPV in relation to climatic cofactors; thereby, setting a platform to devise better intervention measures to combat the epidemics. We conclude that, preventing and controlling RSV infection subsequently reduces the incidence of HMPV.