Stepwise development and mathematical analysis of delayed dengue transmission models with control strategies

Abstract Dengue fever has emerged as a significant global health threat in recent decades, especially in tropical and subtropical regions. Transmitted primarily by the Aedes aegypti mosquito, dengue spreads rapidly in densely populated areas, particularly where water stagnation and inadequate sanitation prevail. In many developing nations, dengue contributes to rising morbidity and mortality, especially among children and young adults, placing a heavy burden on healthcare systems and economies. The recurrent outbreaks and lack of specific antiviral treatment have driven substantial interest in the mathematical modelling and analysis of dengue dynamics and control strategies. To address this issue, our study presents a nonlinear dynamical system with two exponential time delays to examine dengue dynamics, with particular attention to its transmission behaviors, associated risk factors, and possible long-term impacts. This study presents a host-vector structure that includes time delay in human infection. The framework is then extended to account for delays in both human and mosquito dynamics. Mathematical analysis is conducted to derive the basic reproduction number and examine the stability of disease-free (DFE) and endemic equilibria (EE) for both cases. Sensitivity analysis is also performed to investigate how the model parameters with both time delays influence dengue disease transmission and spread in a population. Numerical simulations highlight the significant impact of delays on infection peaks and show that they reduce disease prevalence when implemented effectively. The results emphasize that combining time-delay intervention policies provides a more effective approach for dengue mitigation, offering valuable guidance for public health, specifically in the Malaysian sector and similar tropical and subtropical regions.