In a poultry farm, there are 20,000 chicken to begin with. A disease suddenly breaks out among the chicken. All the chicken are susceptible to this disease which is caused by a deadly virus. If a chicken gets infected, it takes an average of ni 3 days before it exhibits symptoms of the disease and another n2 = 4 days before it dies. The disease is contagious, and may be spread by infected chicken with or without symptoms with equal probability. The likelihood of contact between any two chicken is a = 0.001 contact/chicken? /day. The probability that a healthy chicken gets infected when it comes in contact with an infected chicken is B - 0.01 chicken/contact. Write differential equations that describe the evolution of population of the chicken in various stages of health/sickness. Hint: There will be four categories of chicken: Healthy chicken with population H Infected chicken not exhibiting any symptoms with population Ins Infected chicken with symptoms whose population is Is Dead chicken with population D Write differential equations whose left hand sides are d dIns dIs d dt dt i dt i dt * In a poultry farm, there are 20,000 chicken to begin with. A disease suddenly breaks out among the chicken. All the chicken are susceptible to this disease which is caused by a deadly virus. If a chicken gets infected, it takes an average of ni 3 days before it exhibits symptoms of the disease and another n2 = 4 days before it dies. The disease is contagious, and may be spread by infected chicken with or without symptoms with equal probability. The likelihood of contact between any two chicken is a = 0.001 contact/chicken? /day. The probability that a healthy chicken gets infected when it comes in contact with an infected chicken is B - 0.01 chicken/contact. Write differential equations that describe the evolution of population of the chicken in various stages of health/sickness. Hint: There will be four categories of chicken: Healthy chicken with population H Infected chicken not exhibiting any symptoms with population Ins Infected chicken with symptoms whose population is Is Dead chicken with population D Write differential equations whose left hand sides are d dIns dIs d dt dt i dt i dt *