Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations

The spread of potentially fatal infectious disease is considered in a host population that would increase exponentially in the absence of the disease. Taking into account how the effective contact rate C(N) depends on the population size N, the model demonstrates that demographic and epidemiological conclusions depend crucially on the properties of the contact function C. Conditions are given for the following scenarios to occur: (i) the disease spreads at a lower rate than the population grows and does not modify the population growth rate; (ii) the disease initially spreads at a faster rate than the population grows and lowers the population growth rate in the long run and the following three subscenarios are possible: (iia) the population still grows exponentially, but at a slower rate; (iib) population growth is limited, but the population size does not decay; (iic) population increase is converted into population decrease.