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A model for HIV/AIDS pandemic with optimal control.

Amiru Sule1, Farah Aini Abdullah1

  • 1Pusat Pengajian Sains Matematik, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia.

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|April 8, 2020
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Summary

This study develops a mathematical model for HIV/AIDS, finding the disease-free state is stable if the basic reproduction number (RO) is below one. Optimal control strategies like CD4 counts and treatment were introduced to manage the pandemic.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • The Human Immunodeficiency Virus and Acquired Immune Deficiency Syndrome (HIV/AIDS) pandemic has impacted millions globally since 1981.
  • Understanding disease dynamics is crucial for effective intervention strategies.

Purpose of the Study:

  • To develop and analyze a deterministic mathematical model for HIV/AIDS transmission.
  • To investigate the impact of optimal control strategies on disease management.

Main Methods:

  • Development of a basic deterministic HIV/AIDS model incorporating mass action incidence.
  • Stability analysis of the disease-free equilibrium point using the basic reproduction number (RO).
  • Extension of the model with optimal control theory, including CD4 counts and treatment interventions.

Main Results:

  • The disease-free equilibrium is locally asymptotically stable when RO < 1 and unstable when RO > 1.
  • Numerical simulations illustrate the effectiveness of the proposed optimal control strategies.

Conclusions:

  • The basic reproduction number (RO) is a critical threshold for HIV/AIDS control.
  • Optimal control strategies, including monitoring CD4 counts and implementing treatment, show promise in managing the HIV/AIDS epidemic.