Synergistic modeling of hemorrhagic dengue fever: Passive immunity dynamics and time-delay neural network analysis

Dengue fever poses a formidable epidemiological challenge, particularly for vulnerable groups such as infants. This research paper establishes a mathematical model to describe the dynamics of secondary immunity in infants against dengue hemorrhagic fever, who acquired primary immunity through maternal antibodies. The effect of passive immunity in the form of dengue immunoglobulin is analyzed for high-risk patients for different scenarios, including standard dengue infections, host with pre-existing immunity, delayed diagnosis or treatment, and end-stage dengue cases. Convergence analysis of the model is performed through disease free and disease endemic equilibrium points in terms of basic reproduction number R₀ along with local stability of disease-free equilibrium point. Adams numerical approach is utilized to simulate dengue disease/immunity interactions. A time delay exogenous neural network approach coupled with Levenberg-Marquardt optimization is designed to characterize, model and simulate these curated scenarios. Exhaustive neural network procedures determine the efficacy of the neural network approach by means of mean square error (MSE) loss charts, error correlation graphs, error histogram analysis and time-series prediction charts. The impeccable characterization of the dengue fever scenarios is supported by extremely low MSE results of the order 10^-9 to 10^-11. To further showcase the competency of the neural network predictions, an exhaustive comparative study against the reference numerical solutions is illustrated with absolute errors in the range of 10^-3 to 10^-5. The novel development of mathematical model coupled with time-delay exogenous neural networks significantly enhances our ability to understand and predict the intricate dengue hemorrhagic fever dynamics allowing for targeted interventions for such infectious disease and epidemiological scenarios.