Stochastic budget dynamics

Introduce noise into the deterministic budget dynamics of the epidemic Stackelberg mean-field game to model uncertainty in public-health resource allocation and policy implementation.

Background

The principal's budget is represented by a deterministic state process whose spending rate depends on policy controls and the population state distribution. The authors state that incorporating noise could capture uncertainty arising in public-health resource allocation and policy implementation and identify this stochastic generalization as an open direction.

References

Several interesting directions remain open for future work. First, regarding model formulation, we simplify individual vaccination uptake by treating it as a decision made directly by the principal, in order to focus on the allocation of budget between social distancing and vaccination. A natural extension is to incorporate individual decision-making on vaccination. Second, the budget state process in the current framework is deterministic. Introducing noise into the budget dynamics may capture the uncertainty that arises from public health resource allocation and policy implementation in practice, we plan to address this situation in the general model form.

— Epidemic Control using Stackelberg Mean Field Game with Budget Constraint  (2609.19641 - Liu et al., 17 Sep 2026) in Section 5, Conclusions and Future Directions