### Mathematical Biosciences and Engineering

2013, Issue 4: 959-977. doi: 10.3934/mbe.2013.10.959

# The ratio of hidden HIV infection in Cuba

• Received: 01 August 2012 Accepted: 29 June 2018 Published: 01 June 2013
• MSC : Primary: 34D20, 93E12; Secondary: 92D30.

• In this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for the ratio is derived from a previous HIV/AIDS model, which was proposed for the Cuban case, where active search for infected individuals is carried out through a contact tracing program. The stability analysis proves that the model for the ratio possesses a single positive equilibrium, which turns out to be globally asymptotically stable. The sensitivity analysis provides an insight into the relative performance of various methods for detection of infected individuals. An exponential regression has been performed to fit the known infected population, owing to actual epidemiological data of HIV/AIDS epidemics in Cuba. The goodness of the obtained fit provides additional support to the proposed model.

Citation: Miguel Atencia, Esther García-Garaluz, Gonzalo Joya. The ratio of hidden HIV infection in Cuba[J]. Mathematical Biosciences and Engineering, 2013, 10(4): 959-977. doi: 10.3934/mbe.2013.10.959

### Related Papers:

• In this work we propose the definition of the ratio of hidden infection of HIV/AIDS epidemics, as the division of the unknown infected population by the known one. The merit of the definition lies in allowing for an indirect estimation of the whole of the infected population. A dynamical model for the ratio is derived from a previous HIV/AIDS model, which was proposed for the Cuban case, where active search for infected individuals is carried out through a contact tracing program. The stability analysis proves that the model for the ratio possesses a single positive equilibrium, which turns out to be globally asymptotically stable. The sensitivity analysis provides an insight into the relative performance of various methods for detection of infected individuals. An exponential regression has been performed to fit the known infected population, owing to actual epidemiological data of HIV/AIDS epidemics in Cuba. The goodness of the obtained fit provides additional support to the proposed model.

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