### Mathematical Biosciences and Engineering

2015, Issue 1: 23-40. doi: 10.3934/mbe.2015.12.23

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

• Received: 01 July 2014 Accepted: 29 June 2018 Published: 01 December 2014
• MSC : Primary: 92B05, 92D30; Secondary: 92D25.

• 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.

Citation: Georgi Kapitanov. A double age-structured model of the co-infection of tuberculosis and HIV[J]. Mathematical Biosciences and Engineering, 2015, 12(1): 23-40. doi: 10.3934/mbe.2015.12.23

### Related Papers:

• 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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