Mathematical Modeling of Chickenpox in Phuket: Efficacy of Precautionary Measures and Bifurcation Analysis

Abstract

In this paper, a mathematical model depicting the transmission dynamics of Chickenpox is developed by incorporating a new parameter denoting the rate of precautionary measures. The influence and the importance of following precautionary measures are showed by applying the real data collected at Phuket province, Thailand. The model analysis such as positivity and boundedness of the solutions are provided. The rate of precaution for the spread the of chickenpox was a factor that influenced the basic reproductive number, which was calculated using the next-generation matrix approach. The model's equilibrium points are identified, and the condition for the disease-free equilibrium's local and global asymptotic stability is established. The model also shows forward bifurcation. Numerical simulation is carried out to show the importance of considering the precautionary measures while controlling the disease spread and the influence of those introduced parameters are depicted graphically. Though our results, we concluded that the rate of precautionary measures plays an vital role at the same time it reduces the chance of getting infected by Chickenpox virus.