A mathematical model with degree of risk for Salmonella infections

Salmonella is an important infectious disease of livestock and humans. Reported cases that humans caused by Salmonella have remained high in the world over the past few years. The conventional susceptible-infected-recovery (SIR) models for outbreak analysis of infectious diseases divides the whole population into three groups, a susceptible group, an infected group and a recovery group. In this paper, a new model for the spread of Salmonella is proposed by introducing the degree of risk for the closed population. Unlike the SIR models that only consider the disease transmission among humans, the proposed model with degree of risk also includes and emphasizes both transmission rates from the environment to humans and person to person. In addition, considering the seasonal effect, an improved model based on degree of risk is proposed, where the transmission rate among humans and the degree of risk can be quantified as a function of temperature. The model perdition of the number of infections from 2000 to 2002 is generally in good agreement with the actual observed datasets. Simulation studies show that the proposed models can deal with the pathogen infections like Salmonella with a low transmission rate and a seasonal feature.