<p>Dengue fever is a viral disease, which is transmitted by mosquitoes and can be considered one of the biggest issues of the global population as it endangers more than half of the world population, leading to hundreds of thousands of serious infections and deaths every year, particularly in Malaysia. Nevertheless, the current models tend to ignore the realistic delays in the human infection dynamics and the interaction between them and the intervention strategies, which restricts their usability to the effective control of the outbreak. This paper has extended a nonlinear epidemiological model, which includes an exponential time delay in the human infection process, in order to better manage its transmission. The model comprises of Susceptible, Exposed, Infected and Recovered human classes along with Susceptible and Infected mosquito populations. The most important epidemiological variables such as mosquito reproduction, hospitalization, travel restrictions, and quarantine are combined to assess their impact on disease development, especially in the context of limited effective vaccines. Control strategies such as mosquito repellents and early treatment are examined to assess how delayed implementation influences outbreak severity. The model is analyzed through disease-free (DFE) and endemic equilibria (EE), the basic reproduction number, local and global stability properties, supported by sensitivity analysis to identify influential parameters. Time delay mathematical model and optimal controls have been explored separately for dengue in Malaysia. The integration of a human-specific time delay together with both constant and time-dependent optimal control in the Malaysian context represents the core novelty and significance of this study. The results demonstrate that incorporating time delay significantly alters disease dynamics, including increasing the outbreak peak and delaying epidemic control when interventions are not applied promptly. Furthermore, the combined constant and time-dependent optimal control strategies are shown to substantially reduce infection levels compared to single or delayed interventions. Using Pontryagin’s Maximum Principle (PMP), we derive optimality conditions for the delayed system and identify important and effective strategies to minimize dengue transmission. The non-standard finite difference (NSFD) scheme is used to solve the optimal control problem due to its stability and structure-preserving efficiency. Overall, the findings suggest that early and sustained implementation of combined control strategies is critical for minimizing dengue transmission, especially when intrinsic delays in infection are present. This study highlights the necessity of incorporating time-delay effects into epidemiological models to design more effective and realistic public health interventions.</p>

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Mathematical analysis of dengue dynamics with time delay optimal control strategies

  • Shah Zeb,
  • Siti Ainor Mohd Yatim,
  • Muhammad Rafiq,
  • Waheed Ahmad,
  • Daniyal-Ur-Rehman,
  • Muhammad Sultan Aslam,
  • Baboucarr Ceesay

摘要

Dengue fever is a viral disease, which is transmitted by mosquitoes and can be considered one of the biggest issues of the global population as it endangers more than half of the world population, leading to hundreds of thousands of serious infections and deaths every year, particularly in Malaysia. Nevertheless, the current models tend to ignore the realistic delays in the human infection dynamics and the interaction between them and the intervention strategies, which restricts their usability to the effective control of the outbreak. This paper has extended a nonlinear epidemiological model, which includes an exponential time delay in the human infection process, in order to better manage its transmission. The model comprises of Susceptible, Exposed, Infected and Recovered human classes along with Susceptible and Infected mosquito populations. The most important epidemiological variables such as mosquito reproduction, hospitalization, travel restrictions, and quarantine are combined to assess their impact on disease development, especially in the context of limited effective vaccines. Control strategies such as mosquito repellents and early treatment are examined to assess how delayed implementation influences outbreak severity. The model is analyzed through disease-free (DFE) and endemic equilibria (EE), the basic reproduction number, local and global stability properties, supported by sensitivity analysis to identify influential parameters. Time delay mathematical model and optimal controls have been explored separately for dengue in Malaysia. The integration of a human-specific time delay together with both constant and time-dependent optimal control in the Malaysian context represents the core novelty and significance of this study. The results demonstrate that incorporating time delay significantly alters disease dynamics, including increasing the outbreak peak and delaying epidemic control when interventions are not applied promptly. Furthermore, the combined constant and time-dependent optimal control strategies are shown to substantially reduce infection levels compared to single or delayed interventions. Using Pontryagin’s Maximum Principle (PMP), we derive optimality conditions for the delayed system and identify important and effective strategies to minimize dengue transmission. The non-standard finite difference (NSFD) scheme is used to solve the optimal control problem due to its stability and structure-preserving efficiency. Overall, the findings suggest that early and sustained implementation of combined control strategies is critical for minimizing dengue transmission, especially when intrinsic delays in infection are present. This study highlights the necessity of incorporating time-delay effects into epidemiological models to design more effective and realistic public health interventions.