A Fixed-Point Approach to Mathematical Models in Epidemiology

Pandemics have always posed a great problem in the history of the world, leading to fatal dangers, which is why mathematicians have been challenged to bring their contribution to the management of pandemics, by applying their theoretical paradigms in describing, studying and forecasting their evolution. Compartmental models, i.e. exponential systems, have been remarkable for studying the spread of epidemics. This paper has three objectives: to purpose a generalization of the SEIRV (Susceptible-Exposed-Infected-Recovered-Vaccinated) model for studying the spread of an epidemics and simulation; to present conditions of existence for a solution to the purposed generalized SEIRV model; and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. The conclusions are that, generally, mathematical models with many parameters can be used to forecast epidemics with better accuracy and, also, the elements from the theory of fixed points for multivalued operators can be used for the analysis of epidemics.