## Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations.(English)Zbl 0782.92018

Summary: The spread of a 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 epidemilogical 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.

### MSC:

 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations
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### References:

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