A pandemic model shown as schematic. S(t) is for healthy people's, I(t) is for sick people's and H(t) is for hopsitalized people's total number. ^= Birth rate = Natural Death rate B= transmission infection rate v= hospitalization rate a. Write the function of this model b. v= a and Y(gamma)= . Turn the new functions into dimesionless (dimension free). Make definitions. c. Find the balance points which are virus independent and endemic. On the 3 dimension space, take one point (S, I, H) d. For the balance point( independent from the virus) to be a stable point, find the relation between RO( coefficient of increase) and g. RO=B*^/ (a+ ) g= /(a+ ) For the d part, use the condition of 3x3 Jalcobian matrix's all eigenvalues must be negative. S IL P I Y H H