Analysis of Mathematical Modeling for Chickenpox Disease after Vaccination

Abstract

The chickenpox is a contagious disease caused by the varicella zoster virus (VZV), also known as human herpes virus type 3 (HHV-3), and is called "chickenpox." This type of disease is contagious and transmitted through respiratory droplets, coughing, sneezing, direct contact with an infected person, or sharing contaminated items. Researchers have developed a mathematical model to describe the transmission of chickenpox, considering the disease's incubation period and vaccination at different time intervals. The researchers identified equilibrium points and the conditions that lead to their stability under disease-free and endemic states. These findings were then presented in the form of the basic reproduction number (Basic Reproduction Number : R₀). The stability analysis was then performed under disease-free and epidemic conditions, and the results were consistent with the Routh-Hurwitz criterion. Numerical analysis revealed that the parameters β , α and γ determine whether the basic reproduction value (R₀) will remain in the disease-free state when R₀<1 or in the epidemic state when R₀>1.