A mathematical model of infectious diseases

In the formulation of models for the spread of communicable diseases which include removal and population dynamics, it is necessary to distinguish between removal through recovery with immunity and removal by death due to disease. This distinction must be made because of the difference in the effect on the population dynamics of the different kinds of removal and because there are significant differences in the behavior of the models.We have formulated a class of models which allow recovery with immunity for a fraction of the infective and permanent removal by death from disease for the remainder. Earlier models of this type have postulated an increased death rate for infective, but such models are restricted to exponentially distributed-infective periods. Because of the differences in behavior between models with recovery and models with permanent removal do not arise when the infective period is exponentially distributed, we have chosen to formulate a different type of model which is sufficiently general to admit qualitative differences.

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