Application of Chebyshev Polynomial-Exponential Method and Tamimi-Ansari Method in Dengue Transmission Dynamics: A Comparative Study

Dengue virus transmitted by mosquitoes, poses a significant global health threat, affecting millions of people annually. In this paper, we explore the dynamics of a dengue virus transmission model, structured as an epidemiological mathematical framework. The model divides the total population into seven compartments: susceptible humans S(t), exposed humans E(t), infected humans I(t), recovered humans R(t), susceptible mosquitoes M(t), exposed mosquitoes ME(t), and infected mosquitoes MI(t). We employed the Chebyshev polynomial-exponential method (CPEM) and Tamimi-Ansari method (TAM) to conduct an in-depth semi-analytical examination of this model. The numerical simulation using MATLAB® ode45 solver was used to compare the results with CPEM and TAM, validating the accuracy and effectiveness of the obtained solutions. The comparison shows no significant differences between the CPEM with numerical results, which leads to a interesting findings. Additionally, by varying the sensitive parameters, we analyzed the behavior of the different compartments within the model. This investigation provides valuable insights into the responses of dengue transmission under various conditions, demonstrating the potential of novel semi-analytical methods for studying epidemiological models of infectious diseases, which is highly beneficial for researchers in the field.