Time series non-Gaussian Bayesian bivariate model applied to data on HMPV and RSV: a case of Dadaab in Kenya

Abstract

Background: Human metapneumovirus (HMPV) have similar symptoms to those caused by the respiratory syncytial virus (RSV). The modes of transmission and dynamics of time series data 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. Our objective was to assess the presence of influence of high incidences between the viruses and to ascertain whether higher incidences of one virus are influenced by the other.

Methods: 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.

Results: In this study, our findings showed that RSV incidence contributed to the severity of HMPV incidence. This was achieved through comparison of 12 models with different structures, including those with and without interaction between climatic factors. The models with climatic factors out-performed those without.

Conclusions: 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.

Keywords: Climatic factors; Epidemic; HMPV; Non-Gaussian bivariate Bayesian model; RSV; Time series.

Fig. 1

The monthly counts of epidemics (a) RSV and (b) HMPV plotted against time. The cumulative counts of HMPV cases were approximately 2.5 times less than the RSV counts for the same time-frame

Fig. 2

The monthly counts of RSV and HMPV plotted against time. Overall, the epidemics coincide in timing of their occurrence peaks, especially in March 2011

Fig. 3

Posterior median and point-wise 95% credibility intervals for the best model. Plots showing the Posterior median and point-wise 95% credibility interval of (a) λ_HMPV and (b) ϕ_HMPV for model 6(iii)

Fig. 4

Posterior median values for the priors with Gamma and Beta distributions for the best model. Plots showing the Posterior median values of (a) λ_HMPV and (b) ϕ_HMPV for model 6(iii). Median_Beta and median_Gamma are the posterior medians from the Beta distribution and the Gamma distribution priors respectively

Fig. 5

Posterior median and point-wise 95% credibility intervals for the best model. Plots showing the Posterior median and point-wise 95% credibility interval of (a) τ_{Rainfall _ RSV} and (b) τ_{Rainfall _ HMPV} for model 6(iii)

Fig. 6

Posterior median and point-wise 95% credibility intervals for the best model. Plots showing the Posterior median and point-wise 95% credibility interval of (a) τ_{Wind _ RSV} and (b) τ_{Wind _ HMPV} for model 6(iii)

Fig. 7

Posterior median and point-wise 95% credibility intervals for the best model. Plots showing the Posterior median and point-wise 95% credibility interval of (a) τ_{Dew _ RSV} and (b) τ_{Dew _ HMPV} for model 6(iii)

Fig. 8

Posterior median and point-wise 95% credibility intervals for the best model. Plots showing the Posterior median and point-wise 95% credibility interval of (a) τ_{Visibility _ RSV} and (b) τ_{Visibility _ HMPV} for model 6(iii)