A model of reporting and controlling outbreaks by public health agencies

We study a model of detection and control of an infectious disease by local health agencies in the presence of imperfect information about the likelihood of an outbreak and limited diagnostic capacity that is insufficient to determine the prevalence of disease in all localities in a timely manner. When shared diagnostic capacity is rationed based on reports of symptoms, the decision to report symptoms or not creates a trade-off. On the one hand, rigorous testing of one’s locality allows the health agency in that locality to make an informed disease control decision. On the other hand, reducing the availability of diagnostic capacity for the other localities increases the probability that the disease will spread from an untested area where the disease is not controlled in the absence of more evidence of an outbreak. Symptoms are over-reported (respectively, reported truthfully, or under-reported) when the cost of disease control is sufficiently small (respectively, in some intermediate range, or sufficiently large). The rates of reporting suspicions decrease as the cost of disease control increases because the localities remain exposed more often and the health agencies prefer to reduce the risk of disease transmission by letting other agencies become informed. If the disease incidence decreases or infectiousness increases, symptoms are reported less frequently. If the precision of private signals increases, the extent of over-reporting of symptoms may increase. For different values of the parameters it can be socially optimal to subsidize or tax requests for additional investigations and confirmatory testing.