# Estimating the Size of the HCV Infection Prevalence: A Modeling Approach Using the Incidence of Cases Reported to an Official Notification System

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## Abstract

In this paper we propose two methods to give a first rough estimate of the actual number of hepatitis C virus (HCV)-infected individuals (prevalence) taking into account the notification rate of newly diagnosed infections (incidence of notification) and the size of the liver transplantation waiting list (LTWL) of patients with liver failure due to chronic HCV infection. Both approaches, when applied to the Brazilian HCV situation converge to the same results, that is, the methods proposed reproduce both the prevalence of reported cases and the LTWL with reasonable accuracy. We use two methods to calculate the prevalence of HCV that, as a first, and very crude approximation, assumes that the actual prevalence of HCV in Brazil is proportional to the reported incidence to the official notification system with a constant denoted \(\kappa \). In the paper we discuss the limitations and advantages of this assumption. With the two methods we calculated \(\kappa \), which reproduces both the reported incidence and the size of the LTWL. With the value of \(\kappa \) we calculated the prevalence *I*(*a*) (the integral of which resulted in 1.6 million people living with the infection in Brazil, most of whom unidentified). Other variables related to HCV infection (e.g., the distribution of the proportion of people aged *a* who got infected *n* years ago) can be easily calculated from this model. These new variables can then be measured and the model can be recursively updated, improving its accuracy.

## Keywords

Hepatitis C Mathematical models Notification system incidence Prevalence## Mathematics Subject Classification

92D30## Notes

### Acknowledgments

This work was partially supported by grants from LIM01-HCFMUSP, FAPESP, CNPq and Ministry of Health of Brazil.

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