Modeling salmonellosis transmission dynamics in humans and dairy cattle with optimal controls

In this paper, we develop a mathematical model to examine the transmission dynamics and control analysis of salmonellosis in humans and dairy cattle. The model considers three time-dependent controls (improving hygiene, vaccination, and organic acid disinfectants), human and dairy cattle populations, and Salmonella typhimurium bacteria in the environments and dairy products. The next generation matrix technique is applied to compute the effective reproduction number $R$ that gauges the persistence and extinction of salmonellosis while adopting the proposed control interventions. The stability behavior of the equilibrium states is examined using the Lypunov function method based on the effective reproduction number $R$. The Latin hypercube sampling and the partial rank correlation coefficient methods are used to investigate the sensitivity and uncertainty of input parameters against model outputs. The results indicate that improving hygiene and vaccination can eliminate salmonellosis. Improving hygiene habits at a rate of at least 0.9 per day is recommended to eliminate salmonellosis. An efficacious vaccine that can immunize at least 85% of the vaccinated dairy cattle is also recommended to eradicate salmonellosis if it can be implemented to vaccinate susceptible dairy cattle at a rate of at least 0.45 per day for the first 30 days of the salmonellosis outbreak. The use of all three controls is recommended to eliminate salmonellosis quickly and at the lowest cost.