Dynamical Model for Determining Human Susceptibility to Dengue Fever

Abstract

Problem statement: Mathematical models are a useful tool for understanding and describing the transmission of diseases such as dengue fever, one of the most prevalently emerging diseases common to tropical and subtropical areas throughout South East Asia. By taking into account human susceptibility to disease, the dynamics of a dengue disease model is proposed. Approach: Using standard methods for analyzing a system, the stability of the model is determined by using Routh-Hurwitz criteria. Results and Conclusion: We can show that the basic reproductive number (R₀), the threshold parameter, when R₀<1, the disease-free state is locally asymptotically stable. If R₀>1, the endemic equilibrium state is locally asymptotically stable. Numerical results illustrate the dynamics of the disease within the context of varying parameter values.