A double age-structured model of the co-infection of tuberculosis and HIV

Georgi Kapitanov

doi:10.3934/mbe.2015.12.23

Article Contents

2015, Volume 12, Issue 1: 23-40. Doi: 10.3934/mbe.2015.12.23

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A double age-structured model of the co-infection of tuberculosis and HIV

Georgi Kapitanov^1,

1.
Mathematics Department, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067

Received: June 30, 2014

Revised: September 30, 2014

Published: November 2014

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Abstract

After decades on the decline, it is believed that the emergence of HIV is responsible for an increase in the tuberculosis prevalence. The leading infectious disease in the world, tuberculosis is also the leading cause of death among HIV-positive individuals. Each disease progresses through several stages. The current model suggests modeling these stages through a time-since-infection tracking transmission rate function, which, when considering co-infection, introduces a double-age structure in the PDE system. The basic and invasion reproduction numbers for each disease are calculated and the basic ones established as threshold for the disease progression. Numerical results confirm the calculations and a simple treatment scenario suggests the importance of time-since-infection when introducing disease control and treatment in the model.

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Mathematics Subject Classification: Primary: 92B05, 92D30; Secondary: 92D25.

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