Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics
Abstract
This study establishes theoretical foundations of an adaptive spatial hierarchical Bayesian SEIR model for HIV transmission dynamics. We prove existence and uniqueness of solutions, derive equilibrium conditions, analyze stability properties, and establish convergence guarantees. The enhanced SEIR model incorporates spatial heterogeneity through time-varying connectivity weights and employs hierarchical Bayesian methods for robust parameter estimation. Key results include global existence of nonnegative solutions, stability conditions for disease-free equilibrium, derivation of spatial basic reproduction number R? = ?(FV?¹), and geometric ergodicity of MCMC estimation. Stability analysis demonstrates global asymptotic stability when R? ? 1. These theoretical properties provide rigorous mathematical foundations for HIV control strategies in resource-limited settings.
Keywords
HIV Modeling, SEIR Dynamics, Spatial Epidemiology, Bayesian Inference
Citations
IRE Journals:
Mulati Omukoba Nyukuri , John Sirengo , Lucy Chikamai
"Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics" Iconic Research And Engineering Journals Volume 9 Issue 1 2025 Page 1134-1137
IEEE:
Mulati Omukoba Nyukuri , John Sirengo , Lucy Chikamai
"Theoretical Properties of an Adaptive Spatial Hierarchical Bayesian SEIR Model for HIV Transmission Dynamics" Iconic Research And Engineering Journals, 9(1)
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