Optimal behavioral intervention for a cross-diffusion host-vector model with spatial heterogeneity

Yonghui Ren and Peng Wu

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: Host-vector diseases are widespread in natural environments, and using mathematical models to investigate their transmission mechanisms and propose corresponding control strategies have long been a cutting-edge research focus. In this paper, we construct a general spatio-temporal model for host-vector infectious diseases on a two-dimensional spatial domain. The model incorporates cross-diffusion terms that describe how the diffusive behaviors of individuals influence one another. Our goal is to embed behavioral interventions into the control variables acting on susceptible hosts and vectors, thereby indirectly regulating the dynamics of infected hosts and vectors, an effect that cannot be captured by traditional reaction–diffusion optimal control strategies. Specifically, we first formulate an objective functional to clarify the purpose of adopting optimal control strategies. Next, we prove the uniqueness and essential boundedness of weak solutions to the state system. Then, by establishing the Gateaux differentiability of the control-to-state mapping and introducing the adjoint system, we characterize the optimal behavioral interventions. Finally, numerical experiments validate the theoretical findings and illustrate the impact of optimal interventions on disease spread. The numerical results demonstrate that simultaneously applying behavioral interventions to both hosts and vectors can effectively curb the spatial expansion of the disease.

Keywords: Host-vector disease; Cross-diffusion model; Spatial heterogeneity; Optimal control; Numerical simulations (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008489

DOI: 10.1016/j.chaos.2026.118707

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