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Optimal Eradication of Poliomyelitis

Optimal Eradication of Poliomyelitis. Ryan Hernandez May 1, 2003. Why Poliomyelitis?. characterized by fever, motor paralysis, and atrophy of skeletal muscles (acute flaccid paralysis, AFP)

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Optimal Eradication of Poliomyelitis

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  1. Optimal Eradication of Poliomyelitis Ryan Hernandez May 1, 2003

  2. Why Poliomyelitis? • characterized by fever, motor paralysis, and atrophy of skeletal muscles (acute flaccid paralysis, AFP) • Deemed eradicated in the Americas since 1994, but still a problem in some countries (e.g. Afghanistan, Egypt, India, Niger, Nigeria, Pakistan and Somalia)

  3. What can be done? • Vaccinations • OPV • does not require trained medical staff/sterile injection equipment, live virus could suffer from disease • IPV • Administered through injection only, dead virus, not completely effective

  4. Questions • In the geographical areas where polio still exists, what steps need to be taken to ensure its eradication for each vaccine? • Can we eradicate polio optimally?

  5. Addressing the Questions Eichner and Hadeler develop a deterministic system of differential equations for each vaccine, and perform equilibrium analysis on the system, but no simulations!!!

  6. OPV Model of Eichner and Hadeler

  7. Basic Reproductive Number

  8. Zero vaccination in a developing country?

  9. 10% vaccination

  10. Infected Equilibrium Point

  11. Critical Vaccination Level Rw = 12 Rv = 3 => p* = 0.6875

  12. Critical p*

  13. Optimal Control?

  14. Optimal vaccination:

  15. IPV Model

  16. Basic Reproduction Numbers In our developing country, we have Rw = 12 and R1 = 1.2

  17. Critical vaccination p* = 0.986

  18. Zero vaccination (p=0)

  19. Critical p

  20. Optimal p(t)

  21. Discussion • Furthering the research • a model which combines the two vaccine models into one, two-vaccine model. • consider various population ages, since on national vaccination days, it is usually all children aged 6 and less that are vaccinated. • Possibly consider other forms of optimal control.

  22. Optimal Control! Consider the objective functional: Then the Hamiltonian is as follows: Costate variables satisfy these differential equations:

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