A new delayed SEIR-SEI model for dengue transmission control with sensitivity and competitive mathematical analysis

Dengue fever is a viral illness affecting over ۱۲۹ nations and more than ۵۰% of the global population, causing approximately ۴۰۰ million cases annually. This study explores the mathematical formulation and dynamics of dengue transmission using a structured SEIR-SEI (susceptible human, exposed human, infected human, recovered human, susceptible vector, exposed vector, and infected vector) model, focusing on immunological and delay-based control strategies. An existing nonlinear delayed SEIR-SEI epidemic model is extended to evaluate the effectiveness of awareness, mosquito deterrence, and therapeutic interventions. Rather than immediately resorting to pharmacological methods, the model emphasizes analyzing delay factors due to their significant role in disease control. Since reducing mosquito populations can harm ecological balance, this new approach applies delay-based strategies on human-related factors such as hospitalization, awareness, and travel restrictions to safeguard both public health and the environment. The findings show that the reproductive number alone is insufficient to predict outbreak persistence; recruitment patterns and mosquito biting rates play a more pivotal role. We analyze the model’s mathematical properties, including the reproduction number, equilibrium points, parameter sensitivity, and both local and global stability. Our results demonstrate that model-based strategies focusing on vector control and human behavior effectively reduce dengue transmission. Additionally, we show that the non-standard finite difference scheme outperforms traditional methods like the fourth-order Runge-Kutta in terms of accuracy, stability, and predictive capability. This study offers valuable insights for public health officials and policymakers in designing sustainable strategies to control endemic dengue transmission and prevent future outbreaks.

کلیدواژه ها:

Dengue ، reproductive number ، Global stability ، NSFD ، Convergence analysis