Vector Autoregression Modeling of Malaria Incidence and Mortality Rates in Migori County, Kenya: A Time Series Analysis Incorporating Exogenous Influences

Malaria remains hyperendemic in Kenya’s Lake Victoria basin despite scalable interventions. It is a pressing public health challenge in Migori county that reported a 27% mortality rate in 2020 in children aged 6-59 months, far exceeding national levels. Reports indicate different contributing factors to malaria dynamics in Migori County, including marginal insecticide-treated net (ITN) use, ITN access, effective anti-malaria treatment, and prevalence of malaria infection. The present study seeks to elucidate the temporal interaction between malaria incidence and mortality by employing a range of time series analyses, incorporating exogenous influences by applying classical vector autoregressive (VAR) model to capture lagged dependencies. Further, the study invoked a Bayesian VAR (BVAR) after incorporating exogenous variables for parameter estimating, utilizing Monte Carlo simulations and Gibbs sampling. For model adequacy and forecast accuracy, the analysis made use of Ljung-Box test, partial autocorrelation function, autocorrelation function (ACF), and normality tests among other diagnostic tests. The hierarchical Bayesian vector autoregressive model (BVARX) incorporates monthly incidence and mortality rates (2014-2024, n=120) as the endogenous variables. The exogenous variables comprised ITN access and use, treatment efficacy, and infection prevalence. Ward-level heterogeneity summed the spatial random effects. Hamilton Monte Carlo model estimation with convergence assessed using R ̂<1.01 Counterfactual simulations quantified intervention impacts. ITN use reduced incidence (β = −1.43, 95% CrI: −2.21, −0.65) but access increased mortality (β = 1.81, CrI: 0.32, 3.30), suggesting behavioral misuse. VARX outperformed VAR (WAIC: 412 vs. 587), yet residual spatial autocorrelation (Moran’s I = 0.34, *p* = 0.01) indicated unobserved confounders. BVARX forecasts predicted 22% (CrI: 18–27%) higher incidence by 2025 under current interventions. The regression analysis identified that higher ITN use is significantly associated with reductions in both malaria mortality and incidence. While ITNs and treatments show efficacy, their benefits are eroded by suboptimal utilization and ecological feedback. The study recommended the use of ward-level VARX outputs for geospatial targeting of ITN campaigns as well as integrated resistance monitoring through adaptive Bayesian frameworks.