Development of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV and AIDS Transmission Dynamics in Kenya

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@article{1709800,
      author = {Mulati Omukoba Nyukuri, John Sirengo, Lucy Chikamai},
      title = {Development of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV and AIDS Transmission Dynamics in Kenya},
      journal = {Iconic Research And Engineering Journals},
      year = {2025},
      volume = {9},
      number = {1},
      pages = {1118-1122},
      issn = {2456-8880},
      url = {https://www.irejournals.com/formatedpaper/1709800.pdf},
      abstract = {HIV and AIDS remain a significant public health challenge in Kenya, with 1.3 million people living with HIV and substantial geographic heterogeneity in transmission patterns. Traditional compartmental models inadequately capture spatial-temporal dynamics and adaptive connectivity patterns crucial for effective intervention planning. This study develops an adaptive spatial hierarchical Bayesian SEIR model that integrates transmission patterns, geographic distribution, and robust parameter estimation for HIV and AIDS dynamics in Kenya. The enhanced SEIR framework incorporates five compartments (Susceptible, Exposed, Infected, AIDS, and Treatment) with time-varying spatial weights capturing inter-county connectivity. A three-level hierarchical Bayesian structure provides uncertainty quantification through observation, process, and parameter levels. The spatial component employs Mat?rn correlation with adaptive weights evolving according to distance-decay functions and temporal covariates. Mathematical analysis establishes existence, uniqueness, positivity, and stability properties. The basic reproduction number is derived using next-generation matrix methods, with disease-free equilibrium stability proven for R? < 1. Model validation demonstrates superior performance with geometric ergodicity confirmed for MCMC chains. The framework addresses critical gaps in current HIV modeling by providing dynamic spatial connectivity, multi-level uncertainty quantification, and theoretical rigor. Results indicate the model's potential to improve intervention targeting, optimize resource allocation, and enhance HIV prevention strategies in resource-limited settings.},
      keywords = {HIV Transmission Dynamics, Spatial Hierarchical Bayesian Modeling, SEIR Model, Kenya Epidemiology},
      month = {July},
  }