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Modelling malaria dynamics with partial immunity and protected travellers: optimal control and cost-effectiveness
S Olaniyi1, K O Okosun2,3, S O Adesanya4
1Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
This study models malaria dynamics, finding that protected travelers reduce disease spread. Optimal control strategies are identified to minimize infections and implementation costs for effective malaria prevention.
Area of Science:
- Mathematical modeling
- Epidemiology
- Public health
Background:
- Malaria dynamics are complex, influenced by transient immunity and population movement.
- Understanding disease spread is crucial for effective control strategies.
Purpose of the Study:
- To develop a mathematical model for malaria transmission incorporating transient immunity and protected travelers.
- To analyze the impact of protected travelers on malaria dynamics and identify optimal control strategies.
Main Methods:
- Qualitative analysis of an autonomous mathematical model to identify backward bifurcation.
- Application of optimal control theory to a non-autonomous model with four control variables.
- Cost-effectiveness analysis of combined control strategies.
Main Results:
- Backward bifurcation observed, indicating coexistence of malaria-free and endemic states.
- Increased fraction of protected travelers significantly reduces the basic reproduction number.
- Optimal control strategies involving combinations of interventions are identified for minimizing infection and costs.
Conclusions:
- Protected travelers play a significant role in reducing malaria transmission.
- A combination of control strategies, guided by cost-effectiveness, is essential for sustainable malaria prevention and control.
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