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Analysis and optimal control of an HIV model based on CD4 count.
A Ishaku1,2, A M Gazali1, S A Abdullahi1,3
1Department of Mathematical Science, Bayero University, Kano, Kano State, Nigeria.
Journal of Mathematical Biology
|July 1, 2020
Summary
This study models HIV/AIDS transmission, finding that imperfect education campaigns can worsen outbreaks. Targeted education for new entrants or susceptible individuals is most cost-effective for HIV/AIDS control.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- HIV/AIDS transmission dynamics require sophisticated modeling.
- Classifying infected individuals by CD4 count offers a nuanced approach.
- Intervention strategies like education, testing, and treatment are crucial for control.
Purpose of the Study:
- To develop and analyze a non-linear mechanistic model for HIV/AIDS transmission.
- To investigate the impact of intervention strategies on disease dynamics.
- To identify optimal and cost-effective control strategies.
Main Methods:
- Development of a non-linear mechanistic mathematical model for HIV/AIDS.
- Classification of infected individuals based on CD4 count.
- Incorporation of time-dependent controls for education, testing, and treatment.
- Cost-effectiveness analysis using incremental cost-effectiveness ratio.
Main Results:
- Imperfect public enlightenment campaigns can lead to backward bifurcation, potentially worsening the epidemic.
- Disease-free equilibrium is globally asymptotically stable under certain conditions of campaign effectiveness.
- Optimal control strategies were identified, with education-focused interventions proving highly cost-effective.
- The most cost-effective strategies involve educating newly entrants or a combination of newly entrants and susceptible individuals.
Conclusions:
- Mathematical modeling provides insights into complex HIV/AIDS transmission dynamics.
- Intervention strategies, particularly education, play a vital role in controlling HIV/AIDS.
- Targeted educational campaigns are crucial for cost-effective HIV/AIDS management, with specific recommendations for Nigeria.
