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Optimal control of vertically transmitted disease: an integrated approach
Samit Bhattacharyya1, Suma Ghosh
1Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada. sbhattac@uoguelph.ca
Computational and Mathematical Methods in Medicine
|November 9, 2010
Summary
A mixed strategy of vaccination and antiviral drugs is most effective for controlling diseases with both vertical and horizontal transmission. Cost-effectiveness depends on disease parameters and intervention costs.
Area of Science:
- Epidemiology
- Mathematical Biology
- Control Theory
Background:
- Diseases can spread through parent-to-offspring (vertical) and individual-to-individual (horizontal) transmission.
- Vaccination targets susceptible individuals to reduce horizontal spread.
- Antiviral drugs target infected individuals to reduce vertical transmission.
Purpose of the Study:
- To analyze the cost-effectiveness of disease control strategies.
- To model a disease with both vertical and horizontal transmission dynamics.
- To evaluate the combined impact of vaccination and antiviral treatment.
Main Methods:
- Developed a 3D Susceptible-Infected-Recovered (SIR) model.
- Incorporated vaccination for susceptible individuals.
- Applied antiviral treatment for infected individuals.
- Utilized control theory and Pontryagin's maximum principle for analysis.
Main Results:
- A combined vaccination and antiviral drug strategy, in optimal proportions, proves most effective for disease control.
- The cost-effectiveness of interventions is sensitive to disease parameters.
- Key parameters include force of infection, vertical transmission probability, immunity loss, and treatment costs.
Conclusions:
- Integrated disease control strategies are crucial for managing diseases with dual transmission routes.
- Optimizing the ratio of vaccination to antiviral treatment is key for cost-effective disease management.
- Disease-specific parameters significantly influence the economic viability of control measures.
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