The paper focuses on indirectly infected persons (persons infected by a person, infected by a person, etc., itself infected by a public organism, for AIDS, hepatitis C, etc.). It is assumed that fairness implies the national community to indemnify them. Graph theory is used to explain what is indirect infection. The concept of chains of infection, and their length is central. Re-infections are considered also because even individuals that are initially infected by another cause could become later indirectly infected by the public agent. The number of persons to be indemnified is larger than for direct infection, so the cost of compensation is higher, unless if compensation per capita is lower. The required quantity of information is so large that this is unrealistic and not democratic. The precision of the determination of infecting causes, as well as the responsibility, decreases rapidly when the length of chains increases. With re-infection, potentially all infected persons could become relevant of a compensation. Compensation of indirectly infected persons is unrealistic, what is unfair when the directly infected persons are compensated