Zombie attack. Zombies are attacking a population of humans. In this pop- ulation, people are born naturally at a rate u and die naturally at a rate 8. As the human population defends against the zombies, people kill zombies at a rate 7. In turn, zombies bite people and turn them into zombies at a rate 8 (all rates are per day). Given that the ordinary differential equations for the population of humans (given by P) and the population of zombies (given by Z) are dP = P - BPZ - SP, (1) dt dᏃ -PZ + SPZ, dt (2) write a function named zombie. m that takes as input t (time) and X = [*;*] (column vector of populations) and returns the right-hand side of the ODE system given by Eqs. (1)-(2). Next, write a script, named zombie_main. m that simulates (i. e., solves the ODEs) the following battle scenarios: • Battle 1: 50 zombies vs. 1,000 humans, for tmax = 28 days, with p = 0.010, 8 = 0.001, B = 0.002 and 7 = 0.0015. • Battle 2: 50 zombies vs. 1,000 humans, for tmax = 28 days, with p = 0.010, 8 = 0.001, B = 0.002 and 9 = 0.0019 • Battle 3: 50 zombies vs. 1,000 humans, for tmax = 28 days, with u = 0.010, 8 = 0.001, B = 0.002 and 9 = 0.0022 (Higher y values correspond to humans killing zombies at a higher rate). Notice that you must call the function ode45() for each battle (i. e., three times). Still inside your script zombie_main. m, plot the resulting curves of the two populations (zombies and humans) over the time interval of 28 days for each battle, and include a legend (to identify which curve is P and which is Z). Use one figure per battle.