West Nile Virus

I like to refer to the West Nile Virus as a game and there are 4 types of players that will focus on today.

• Susceptible birds
• Susceptible mosquitoes
• Infected birds
• Infected mosquitoes

With West Nile Virus, susceptible birds get the disease when infected mosquitoes bite them. Susceptible mosquitoes get West Nile Virus when they bite infected birds.

If we assume:

1. A susceptible mosquito bites a bird every three days (or a susceptible mosquito has a 1/3 chance of biting a bird),
2. If the bird is infected, the mosquito that bites the bird has a 20% chance of becoming infected (or 1/5 of the time, they become infected)
3. Depending on the temperature, it takes 10-14 days for the virus to grow in an infected mosquito to the point it can infect birds.
4. The mosquito has no preference for sick birds so the chances of biting an Infected bird is (Infected Birds) / (Birds)

Then the number of mosquitoes that become infected is:

Can you write an equation for the infection of susceptible birds. You will have to make assumptions on how often each bird is bitten and how often bites by infected mosquitoes infect the bird.

The model also has these assumptions.

• Mosquitoes are most active from June through September, so the model has 4 months of 30 days each.
• Some birds die from the disease instead of recovering. Birds that are dying are infected longer than birds that recover. If there is less standing water, the birds all stay closer together, near the water, so the disease spreads faster.
• Some mosquitoes die from natural causes between the time they are infected and the time they begin infecting the animals they bite. The temperature affects how long it takes until an infected mosquito begins infecting the animals they bite. When it is warmer, mosquitoes can be infectious for twice as many days.
• The temperature and amount of standing water affect how many mosquitoes there are. Mosquitoes are born to replace those who die. New mosquitoes are susceptible.

If there are lots of new mosquitoes and one mosquito bites you, is it more or less likely that the mosquito was infected? Hint: How does the ratio (infected mosquitoes) / (infected mosquitoes) + (susceptible mosquitoes) change.

If a higher percentage of birds die, is it more or less likely that a mosquito will bite an infected bird? Hint: How does the ratio (infected birds / number of birds) change?

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