6. Members of an indefinitely large population are either immune to a given disease or are suscep...
6. Members of an indefinitely large population are either immune to a given disease or are susceptible to it. Let X, be the number of susceptible members in the population at time period n and suppose Xo0 and that in the absence of an epidemic X1-X. +1. Thus, in the absence of the disease, the number of susceptibles in the population increases in time, possibly owing to individuals losing their immunity, or to the introduction of new susceptible members to the population. But in each period there is a constant but unknown probability p of a pandemic disease. When the disease occurs all susceptibles are stricken. The disease is non-lethal and confers immunity, so that if T is the first time of disease occurrence, then XT. Compute the stationary distribution for (%).
6. Members of an indefinitely large population are either immune to a given disease or are susceptible to it. Let X, be the number of susceptible members in the population at time period n and suppose Xo0 and that in the absence of an epidemic X1-X. +1. Thus, in the absence of the disease, the number of susceptibles in the population increases in time, possibly owing to individuals losing their immunity, or to the introduction of new susceptible members to the population. But in each period there is a constant but unknown probability p of a pandemic disease. When the disease occurs all susceptibles are stricken. The disease is non-lethal and confers immunity, so that if T is the first time of disease occurrence, then XT. Compute the stationary distribution for (%).