Question

help me solve this transition matrix question. Out of a population of 7 billion people, k1 people have no symptoms, k2 people have mild symptoms, k3 people have severe symptoms and k4 people are zombies(where k1+k2+k3+k4=7 billion). Find values (if they exist) for k1, k2, k3, k4 such that in the long run, the non-zombie population of the earth is non-zero. The transition matrix picture is provided below.