On the Spread of Epidemics by Carriers

Quantitative problems in the phenomenon of epidemnics have been of interest for over fifty years. Specific applications of the theoretical developments have been made to malaria (Ross [1911]; Martini [1921]), to measles (Wilson et al. [1939]; Bartlett [1957]), and to other communicable diseases. Specific references may be found in the excellent monograph by Bailey [1957]. All of the diseases whose theory has been developed so far are such that a population can be divided into subpopulations whose members are considered to be susceptible, infected, or imnmune. However, there are several diseases in which carriers are a significant factor in the spread of the epidenmic. The prime example of these is typhoid, although carriers may be important in the spread of bilharzia, amoebic dysentery, and typhus. A carrier is defined to be an individual who does not have overt disease symptoms but nevertheless is able to communicate the disease to others. Under this category we may include not only human carriers but also inanimate sources of disease such as polluted streams which may be used by a fairly large population. Diseases involving carriers are still important notwithstanding modern health controls-as witness the recent outbreak of typhoid in Zermatt, Switzerland. In more primitive societies the problem can obviously be more acute. To date, no theory seems to have been developed to make quantitative the factors involved in a carrier-borlne disease. It is the purpose of this paper to analyze a fairly simple and admittedly incomplete model of an epidemic involving carriers. I will assume in the present work, that only carriers are responsible for the spread of the disease. By implication this assunmes that public health measures are efficient enough to isolate infected individuals who may be able to transmit the disease to others. This may not be as unrealistic as it sounds. Consider, for example, the case of typhoid. It is estimated that about one or two percent of all those who have re-

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