The most prevalent health issue is salmonella infection. Every year, between 200 million and 1.3 billion people are infected with Salmonella. Salmonella spreads by direct animal contact, food and drink, and very infrequently, person-to-person contact via the fecal-oral route. It is estimated that 94% of salmonellosis transmission occurs through food. Salmonella infection is, in fact, a bacterial infection. It is crucial to utilize mathematical modeling to describe how biological and biomedical systems behave dynamically. The SIRS model of epidemics is the most often used mathematical model. Describing the patterns of Salmonella infectious disease in animal populations and the human population, we have formulated a SIRS epidemic model in our work. In significant part, the model was developed as a collection of ODEs based on the traits of transmission of infection. The occurrence of infection-free and endemic stable states was initially noted, and stability of the critical points of the model was later proven (infection-free and endemic). Following that, the fundamental reproduction number was calculated using the method of a next-generation matrix. Finally, the numerical simulations of this SIRS model have been completed. The analytical finding is explained using numerical simulations.