Hamilton Jacobi Bellman optimization for mpox epidemics: a fractional-order stochastic model integrating zoonotic, environmental, and human transmission

Abstract

The Monkeypox (mpox) represents a major public health threat, particularly in endemic regions like the Democratic Republic of Congo (DRC), where zoonotic spillover, environmental persistence, and human to human transmission drive the epidemic cycle. We propose a 10 compartment fractional order stochastic model integrating human, zoonotic, and environmental transmission pathways with stochastic optimal control via Hamilton Jacobi Bellman (HJB) theory. For the model calibration, we used 25 years of weekly mpox incidence data from the DRC (86,798 cases, 1,302 observations). Zoonotic spillover accounted for approximately 15% of transmission (\(\beta_2 = 0.18day^{-1}\)), while environmental pathogen persistence averages 2 days (\(\xi = 0.47day^{-1}\)). We derived cost optimal intervention policies which minimize disease burden and intervention costs through dynamic programming. The HJB framework identified synergistic combined strategies, moderate vaccination coupled with aggressive quarantine which reduce final endemic prevalence by 78% (from 847 to 189 infections), substantially outperforming either intervention alone. Sensitivity analysis via Sobol' indices identifies human to human transmission and fractional order as dominant variance drivers, together explaining 65% of output uncertainty. Scenario modeling demonstrated that increased zoonotic spillover doubles endemic prevalence, improved detection necessitates 50% quarantine expansion, and treatment breakthroughs permit resource reallocation from isolation to prevention. Our work demonstrates that fractional order formulations capture observed epidemic inconsistency better, with long range temporal dependence, and power law spectral scaling compared to standard integer order models. This work provides evidence based recommendations for resource allocation in limited resource settings.