Three-level global resource allocation model for HIV control: <em>A hierarchical decision system approach</em>

Semu Mitiku Kassa; Semu Mitiku Kassa

doi:10.3934/mbe.2018011

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 1: 255-273. doi: 10.3934/mbe.2018011

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Three-level global resource allocation model for HIV control: A hierarchical decision system approach

Semu Mitiku Kassa ^1,2

1.
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology (BIUST), P/Bag 16, Palapye, Botswana
2.
Department of Mathematics, Addis Ababa University, P.O.Box 1176, Addis Ababa, Ethiopia

Received: 24 August 2016 Revised: 03 March 2017 Published: 01 February 2018
MSC : Primary: 92B05, 92D30, 90B50, 91A80; Secondary: 34B60, 91A10, 90C31, 00A71

Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources. In this paper, a hierarchical mathematical optimization model is proposed to solve such a problem. Combining existing epidemiological models with the kind of interventions being on practice, a 3-level hierarchical decision making model in optimally allocating such resources has been developed and analyzed. When the impact of antiretroviral therapy (ART) is included in the model, it has been shown that the objective function of the lower level decision making structure is a non-convex minimization problem in the allocation variables even if all the production functions for the intervention programs are assumed to be linear.
- Multilevel resource allocation,
- hierarchical planning,
- epidemiological modeling,
- HIV,
- hierarchical optimization
Citation: Semu Mitiku Kassa. Three-level global resource allocation model for HIV control: A hierarchical decision system approach[J]. Mathematical Biosciences and Engineering, 2018, 15(1): 255-273. doi: 10.3934/mbe.2018011

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Abstract

Funds from various global organizations, such as, The Global Fund, The World Bank, etc. are not directly distributed to the targeted risk groups. Especially in the so-called third-world-countries, the major part of the fund in HIV prevention programs comes from these global funding organizations. The allocations of these funds usually pass through several levels of decision making bodies that have their own specific parameters to control and specific objectives to achieve. However, these decisions are made mostly in a heuristic manner and this may lead to a non-optimal allocation of the scarce resources. In this paper, a hierarchical mathematical optimization model is proposed to solve such a problem. Combining existing epidemiological models with the kind of interventions being on practice, a 3-level hierarchical decision making model in optimally allocating such resources has been developed and analyzed. When the impact of antiretroviral therapy (ART) is included in the model, it has been shown that the objective function of the lower level decision making structure is a non-convex minimization problem in the allocation variables even if all the production functions for the intervention programs are assumed to be linear.

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