Question

Two evil men (Bob and Cata) from LA invented a new virus called COVID-22 and released it to Vieux Hull where people have very suspicious and moistly hygiene habits. But Super Angie is there to protect the citizens by teaching better hygiene habits, enforcing social distancing measures and distributing vaccines. The population can be divided into four categories using the NIRD model; - n_k = proportion of non-infected people in k weeks. - i_k = proportion of infected people in k weeks. - r_k = proportion of recovered (or immuned) people in k weeks. - d_k = proportion of dead people in k weeks. Thus initially nobody is infected. According to data, it is estimated that; - 4% of the non-infected people get infected the week after. - 20% of the non-infected people will receive the vaccine (thus they become immuned (recovered) the week after). - 60% of the people infected recover the week after. - 5% of the people infected die the week after. - The recovered stay recovered (can't be infected again) and the dead stay dead (no zombies). For k ? 0, let x_k = [n_k, i_k, r_k, d_k]^T a) Find the Markov matrix M such that x_{k+1} = Mx_k and give the initial condition x_0. b) What will be the percentage of people death in 3 weeks?

          Two evil men (Bob and Cata) from LA invented a new virus called COVID-22 and released it to Vieux Hull where people have very suspicious and moistly
hygiene habits. But Super Angie is there to protect the citizens by teaching better hygiene habits, enforcing social distancing measures and distributing
vaccines.

The population can be divided into four categories using the NIRD model;
- n_k = proportion of non-infected people in k weeks.
- i_k = proportion of infected people in k weeks.
- r_k = proportion of recovered (or immuned) people in k weeks.
- d_k = proportion of dead people in k weeks.

Thus initially nobody is infected.

According to data, it is estimated that;
- 4% of the non-infected people get infected the week after.
- 20% of the non-infected people will receive the vaccine (thus they become immuned (recovered) the week after).
- 60% of the people infected recover the week after.
- 5% of the people infected die the week after.
- The recovered stay recovered (can't be infected again) and the dead stay dead (no zombies).

For k ? 0, let

x_k = [n_k, i_k, r_k, d_k]^T

a) Find the Markov matrix M such that x_{k+1} = Mx_k and give the initial condition x_0.
b) What will be the percentage of people death in 3 weeks?

Two evil men (Bob and Cata) from LA invented a new virus called COVID-22 and released it to Vieux Hull where people have very suspicious and moistly
hygiene habits. But Super Angie is there to protect the citizens by teaching better hygiene habits, enforcing social distancing measures and distributing
vaccines.

The population can be divided into four categories using the NIRD model;
- nk = proportion of non-infected people in k weeks.
- ik = proportion of infected people in k weeks.
- rk = proportion of recovered (or immuned) people in k weeks.
- dk = proportion of dead people in k weeks.

Thus initially nobody is infected.

According to data, it is estimated that;
- 4% of the non-infected people get infected the week after.
- 20% of the non-infected people will receive the vaccine (thus they become immuned (recovered) the week after).
- 60% of the people infected recover the week after.
- 5% of the people infected die the week after.
- The recovered stay recovered (can't be infected again) and the dead stay dead (no zombies).

For k ? 0, let

xk = [nk, ik, rk, dk]^T

a) Find the Markov matrix M such that xk+1 = Mxk and give the initial condition x0.
b) What will be the percentage of people death in 3 weeks?

Added by Josefina M.

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