Journal of Prime Research in Mathematics

# A fixed-point approach to a multi-group SEIRV epidemic model

Amelia Bucur$$^{a,*}$$

$$^a$$Department of Mathematics and Informatics, Faculty of Sciences, Lucian Blaga University of Sibiu, Sibiu, Romania.

Correspondence should be addressed to: amelia.bucur@ulbsibiu.ro

### Abstract

Epidemics was always great problems in the human history and mathematicians have been challenged to bring their contribution to the management of epidemics, by using their abstract concepts in studying and forecasting their evolution. Compartmental models, have been remarkable for analysis the spread of epidemics. This paper has three objectives: to purpose a multi-group SEIRV epidemic model for studying the spread of an epidemics, to present conditions of existence for a solution to the purposed generalized SEIRV model and an example of simulations. The principal conclusion is that, the theory of fixed points can be used for the analysis of epidemics. The results of this paper adapt the results obtained in (Bucur, 2022, in International Journal of Advance Study and Research Work (IJASRW) 5(11)) and in (Guran, Bota and Naseem, 2020, in Symmetry 12, 856) to a generalization of the SEIR model.

#### Keywords:

mathematical modeling; epidemiological dynamics; fixed.