A Mathematical Approach to Characterize the Transmission Dynamics of the Varicella-Zoster Virus

Maria Gommel, Sam Jaros, Donglun Liu

Abstract


The Varicella-Zoster Virus (VZV) is the cause of chickenpox and shingles in humans. Chickenpox is generally a mild disease affecting children under thirteen, but is much more dangerous if contracted at an older age. Complications from chickenpox include encephalitis, pneumonia, bronchitis, cerebral ataxia, congenital varicella syndrome, and Reye’s syndrome. Shingles generally affects older or immunocompromised people, and is characterized by a painful rash. Complications include glaucoma, blindness, post-herpatic neuralgia, or encephalitis. In the U.S., the chickenpox vaccine was added to the national immunization program in 1995. This one dose policy effectively decreased incidences, but failed to prevent outbreaks. The two-dose vaccination program was adopted in 2007. A shingles vaccine exists and is recommended for people over sixty as a booster shot, but it is only about 50% effective. The question now is whether an effective vaccination program for chickenpox would increase the

incidence of shingles due to the lack of adult exposure to VZV.

Mathematical modeling is used to investigate VZV

transmission in the US population as well as the effectiveness of various control measures. Their effectiveness in preventing outbreaks was investigated, and four streamlined models were developed to describe the spread of chickenpox and shingles, and the models’ basic epidemic characteristics, such as equilibrium solutions and their stability, were analyzed. In addition, the Vaccination Reproduction Number (Rv) was calculated for each model using the Next Generation Operator Method. Numerical solutions for various values of parameters are investigated in the attempt to predict the efficacy of various vaccination strategies within a population as well as view the long- term behavior of shingles incidence in conjunction with these vaccination strategies for VZV. The result from numerical solutions shows that with 2-dose program and 90% coverage, the zoster incidence will increase significantly for about 27 years, and then decrease after that.


Keywords


Epidemiology; Mathematical Modeling; Chickenpox

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