Joint estimation of stochastic transmission-rate process and intervention function from data

Develop robust statistical estimation methods to jointly recover the parameters of the Cox–Ingersoll–Ross (CIR) or Jacobi transmission-rate process P_t and the deterministic intervention function φ(t) from empirical epidemic datasets in the stochastic SI model with transmission rate β_t = φ(t) P_t and susceptible dynamics dS_t/dt = −β_t S_t (1 − S_t).

Background

The paper models the SI epidemic with a stochastic transmission rate β_t = φ(t)P_t, where P_t is either a Cox–Ingersoll–Ross (CIR) process or a Jacobi process, and φ(t) is a deterministic function representing interventions. Theoretical results focus on asymptotic behavior via the integrated intensity H_t = ∫_0t β_s ds and provide analytical tools particularly for the CIR case without intervention.

While the modeling and asymptotic analysis are developed, the authors highlight that, in practical applications, one must infer both the parameters of the stochastic process P_t and the intervention function φ(t) from observed epidemic data. They explicitly state this as an open problem, emphasizing the need for robust estimation techniques capable of disentangling intrinsic stochastic transmission dynamics from deterministic intervention effects.

References

Despite these insights, several statistical open problems remain to be addressed in future work. For instance, given an empirical epidemic dataset, can we develop robust estimation techniques to recover both the underlying process parameters and the deterministic intervention function?

— Modeling Transmission Intensity in SI Epidemics via CIR and Jacobi Processes: Asymptotic Results and Preliminary Intervention Strategies  (2604.02224 - Cataño et al., 2 Apr 2026) in Discussion and Conclusions (Section: Discussion and Conclusions)