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Mathematical analysis of a model for AVL-HIV co-endemicity
N Hussaini1, J M-S Lubuma2, K Barley3
1Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa; Department of Mathematical Sciences, Bayero University Kano, P.M.B. 3011, Kano, Nigeria.
Mathematical Biosciences
|November 25, 2015
Summary
This study models Anthroponotic Visceral Leishmaniasis (AVL) and human immunodeficiency virus (HIV) co-transmission, finding both diseases can persist together. AVL can invade HIV-endemic states, highlighting the importance of understanding disease dynamics.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Anthroponotic Visceral Leishmaniasis (AVL) and human immunodeficiency virus (HIV) are significant global health concerns.
- Understanding the interplay between vector-borne and sexually transmitted infections is crucial for effective control strategies.
Purpose of the Study:
- To develop and analyze a mathematical model for the co-transmission dynamics of AVL and HIV.
- To assess the impact of each disease on the overall transmission and identify key driving parameters.
Main Methods:
- A compartmental mathematical model was developed to simulate AVL and HIV transmission.
- Uncertainty and sensitivity analyses were performed using Ethiopian epidemiological data.
- Numerical simulations were conducted to explore disease co-existence and invasion scenarios.
Main Results:
- The AVL component exhibits backward bifurcation. Key drivers for AVL are sandfly biting rate, vector capacity, and transmission probability.
- Key drivers for HIV are transmission rate, HIV-induced death rate, and infectiousness of AIDS individuals.
- For the co-transmission model, HIV transmission rate, sandfly biting rate, and HIV-induced death rate are dominant.
Conclusions:
- Both AVL and HIV can co-exist, with AVL potentially dominating but not eradicating HIV.
- AVL can invade a population with an existing HIV endemic state if the invasion reproduction number exceeds unity.
- The model provides insights into the complex dynamics of co-infections and informs public health interventions.
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