Mathematical analysis of a methicillin-resistant Staphylococcus aureus model in hospitals and the community

Abstract

In this paper, we study a methicillin-resistant Staphylococcus aureus epidemic model taking into account both hospitals’ and the general community dynamics. The model is designed to track the long-term dynamics of methicillin-resistant Staphylococcus aureus infections. Mathematical analysis of the developed model is carried out. The MRSA-free equilibrium M^o_a and the model reproduction number R₀ are established. Numerical simulations are performed using previously published data from relevant scientific literature. It is shown that both the MRSA-free equilibrium and the MRSA-persistent equilibrium are locally asymptotically stable when R₀<1 and R₀>1, respectively. Numerical simulations are also conducted to ascertain the effects of variations in key parameter values on specific compartments: (i) hospitalized individuals exclusively, (ii) the general community exclusively, or (iii) both hospitalized individuals and the general community concurrently. It is shown that 1% increase in the values of β_h and β_c corresponds to approximately 27.1% and 8.3% increase in the value of R₀, respectively. On the other hand, a 0.1% increase in the values of ε and ψ, and a 0.25% increase in the value of δ corresponds to approximately 0.53%, 0.498% and 0.267% decrease in the value of R₀, respectively. The findings suggest the need for policymakers to implement robust measures aimed at minimizing infection transmission between both infected and susceptible individuals, encompassing both nosocomial environments and the wider community.