Optimal vaccination strategies and rational behaviour in seasonal epidemics
| Autor: | Paula Rodrigues, Maria do Céu Soares, Fabio A. C. C. Chalub, Paulo Doutor |
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| Rok vydání: | 2015 |
| Předmět: |
0301 basic medicine
Computer science Transmission rate Disease free 01 natural sciences Choice Behavior 03 medical and health sciences Econometrics Humans Artificial induction of immunity 0101 mathematics Quantitative Biology - Populations and Evolution Epidemics Population Density Models Statistical Applied Mathematics 010102 general mathematics Vaccination Populations and Evolution (q-bio.PE) Agricultural and Biological Sciences (miscellaneous) Systemic Inflammatory Response Syndrome 3. Good health 030104 developmental biology FOS: Biological sciences Modeling and Simulation 92D30 91A99 34A34 Seasons Epidemic model |
| Zdroj: | Journal of mathematical biology. 73(6-7) |
| ISSN: | 1432-1416 |
| Popis: | We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal vaccination, in the sense that it minimizes the effort of vaccination in the set of vaccination strategies for which, for any sufficiently small perturbation of the disease free state, the number of infectious individuals is monotonically decreasing; ii) Nash-equilibria strategies where all individuals simultaneously minimize the joint risk of vaccination versus the risk of the disease. The former case corresponds to an optimal solution for mandatory vaccinations, while the second correspond to the equilibrium to be expected if vaccination is fully voluntary. We are able to show the existence of both an optimal and Nash strategies in a general setting. In general, these strategies will not be functions but Radon measures. For specific forms of the transmission rate, we provide explicit formulas for the optimal and the Nash vaccination strategies. 27 pages, 4 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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