Role of relapse and multiple time delays in shaping Nipah virus epidemic dynamics: a mathematical modeling study

Nipah virus (NiV) is a sporadic yet extremely deadly zoonotic pathogen, with reported case fatality rates of 40%-75% in impacted areas. Prolonged incubation, documented relapse, and delayed-onset encephalitis following apparent recovery indicate that NiV dynamics are influenced by intricate temporal processes. However, mechanistic contributions of these processes to epidemic persistence remain poorly understood. In this study, we develop and analyze a delay differential equation model for NiV transmission that explicitly incorporates incubation delay, relapse, and post-recovery delay effects. We compute a primary-transmission reproduction threshold (R0), characterize the disease-free and endemic equilibria, and analyze their stability, including delay-induced Hopf bifurcations. We show that relapse modifies the endemic-equilibrium existence condition, so an endemic equilibrium is not determined solely by the classical threshold criterion R0 = 1. We calibrate the model to NiV incidence data from Bangladesh (2001-2024) and perform simulations and sensitivity analyses to evaluate the effects of relapse and delays across epidemiological scenarios. Results indicate that sustained oscillations occur only under hypothetical parameter regimes, suggesting that delay-induced periodic outbreaks are unlikely under empirically informed conditions. Scenario analyses demonstrate that relapse and encephalitis-related delays predominantly influence post-peak dynamics, while incubation delay alters the time and intensity of the epidemic peak. We also introduce a relapse-driven replenishment fraction to quantify contribution of relapse to continued transmission, demonstrating its growing significance following the first outbreak peak. Overall, our results identify relapse as a key mechanism for epidemic persistence and underscore the importance of incorporating relapse and biological time delays into epidemiological modeling and public health strategies.