Limiting dengue transmission using a differential game approach

Abstract

In this paper, a fundamental structural asymmetry in dengue fever epidemic control approaches is identified and formalized. We show that treatment and quarantine interventions must influence the sick compartment, whereas the majority of epidemic game models treat interventions as affecting the susceptible compartment (e.g., vaccination). A fundamental imbalance is produced by this structural difference: public health interventions (downstream) alter the linear elimination term, whereas behavioral control (upstream) alters the bi linear incidence term. We demonstrate through careful mathematical analysis that behavioral control has a greater global impact through multiplicative effects over time, while public health measures dominate in local immediate sensitivity. For a differential game model, we calculate the open-loop Nash equilibrium and demonstrate an 86.4% decrease in peak infections when compared to no control. Our findings show that where control enters the epidemic system is just as important as how much control is applied, resolving the apparent dichotomy between local sensitivity and global impact. The best dengue management methods are significantly impacted by this structural asymmetry.