Differential equation compartmental models are invaluable tools used to forecast and analyze disease trajectories. Of these models, the subclass dealing only with susceptible and infectious individuals provides a rare and extremely useful example where solutions have a closed-form expression, as represented by the logistic equation. However, the logistic equation is limited in its capacity to describe disease trajectories, as its solutions must monotonically converge to either the disease-free equilibrium or endemic equilibrium, depending on parameters. Unfortunately, many diseases undergo periodic cycles and therefore do not converge to any equilibria. To address this limitation, we developed a generalized susceptible-infectious-susceptible compartmental model capable of describing both periodic and non-periodic disease trajectories built directly from an infectious period distribution. To demonstrate our approach, we apply the model to predict gonorrhea incidence in the US, and illustrate how model parameters affect the behavior of the system. The significance of our work is that we provide a novel susceptible-infected-susceptible model whose solution has a closed-form expression, which could be periodic or non-periodic, depending on model parameterization. Because of this, the work provides disease modelers with a simple means to investigate the potential periodic behavior of many diseases, and thereby aids in ongoing initiatives to curtail recurrent outbreaks.

This article refers to the issues associated with the crucial significance of the interpretation of tax law provisions made by administrative courts in the course of the judicial inspection of tax decisions, within the context of protecting the subjective rights of taxpayers. The analysis in that regard has been prepared based on the provisions of art. 153 of the Act of 25 July 2002 on Proceedings before Administrative Courts, which expresses the important rule of binding the court and the administrative authority, whose act was the subject of an appeal, with a legal assessment and instructions regarding the further proceedings described in the decision of the administrative court. As a result of this rule, a decision of an administrative court exerts the results exceeding the scope of judicial administrative proceedings, while its effect also covers the future tax proceedings. If the legal assessment made by the court refers to the regulations that affect the subjective rights of a taxpayer, it means that the administrative court imposes the effects of “its” interpretation of those provisions on a tax authority. In turn, the tax authority is obliged to respect those rights in accordance with the opinions of the court, which usually affects the final resolution of a tax case. It should be borne in mind that a taxpayer, by submitting an appeal against a tax decision to an administrative court, demands not only an inspection of the acts of tax administration, but also - which should be emphasized - demands the execution of its rights, including its subjective rights. Therefore, we should not forget the crucial role of the administrative courts in the protection of the substantive rights of taxpayers. The instrument that allows the administrative courts to guard the subjective rights of taxpayers, consists in the procedural regulations included in the provisions on proceedings before administrative courts, and in particular art. 153 of the Act on Proceedings before Administrative Courts in Poland.