A Theoretical Model for Optimal Fluid Maintenance in Clinical Dengue Patients

Dengue is one of the most widespread vector-borne diseases, with no specific medical treatment for a cure. In some cases, dengue infection progresses to hemorrhagic shock, a life-threatening condition that requires immediate medical intervention. At this critical stage, the timely infusion of intravenous fluids is essential for patient survival. However, unsystematic fluid administration can result in fluid overload and lead to adverse outcomes. In this study, we extend a minimal within-host dengue model to incorporate both plasma dynamics and intravenous fluid infusion. Using hematocrit level data from hospitalized dengue patients, collected between days 5 and 14 after the onset of fever, we estimate parameters related to intravenous fluid leakage via the Maximum Likelihood Estimation method. To determine the optimal fluid infusion strategy, we apply optimal control theory, proving the existence of a time-dependent optimal infusion strategy. The model is solved numerically using the forward-backward sweep method to determine the optimal fluid infusion rate. Our results indicate that, in contrast to the WHO guidelines, which recommend initiating fluid therapy at the highest infusion rate followed by a gradual taper, the optimal strategy begins with a lower infusion rate, increases gradually during the first 24 hours, and subsequently tapers off. Despite this markedly different infusion profile, the proposed strategy successfully maintains the plasma deficit within a clinically feasible range throughout treatment, thereby preventing the onset of shock. Furthermore, our analysis reveals that a broad range of infusion strategies can achieve the same therapeutic objective, allowing fluid administration to be tailored to the patient's clinical condition and the physician's judgment. The results also indicate the critical need for timely fluid therapy, demonstrating that fluid requirements rise significantly with delayed treatment. Additionally, the uncertainty regarding restoration increases with prolonged delays. While delays of a few hours in initiating fluid support can be compensated for, delays exceeding one day could be life-threatening.