Mathematical Model of the Impact of a Nonantibiotic Treatment for Clostridium difficile on the Endemic Prevalence of Vancomycin-Resistant Enterococci in a Hospital Setting

Figure 1

Schematic diagram of the patient compartments. CDAD = clostridium difficile-associated disease; CDAD+ = clostridium difficile-associated disease positive; CDAD− = clostridium difficile-associated disease negative; VRE = vancomycin-resistant enterococci; VRE+ = vancomycin-resistant enterococci colonized; VRE− = vancomycin-resistant enterococci not colonized; AB− = off antibiotics; AB+ = on antibiotics; 𝜆^off_𝑈− = CDAD−, uncolonized, off antibiotic: admission rate; 𝛾^off_𝑈−= CDAD−, uncolonized, off antibiotic: average length of stay; 𝜆^on_𝑈−= CDAD−, uncolonized, on antibiotic: admission rate; 𝛾^on_𝑈−= CDAD−, uncolonized, on antibiotic: average length of stay; 𝜏^stop_𝑈−= CDAD−, uncolonized, on antibiotic: stop antibiotic; 𝜏^start_𝑈−= CDAD−, uncolonized, off antibiotic: start antibiotic; 𝛿^off_𝑈+= CDAD+, uncolonized, off antibiotic: transit to CDAD−; 𝜎 = fraction of AB patients that transit to CDAD+ and stop AB; 𝜔^on_𝑈−= CDAD−, uncolonized, on antibiotic: transit to CDAD+; 𝛿^on_𝑈+= CDAD+, uncolonized, on antibiotic: transit to CDAD−; 𝛼^on_𝑈+= average number of contacts between uncolonized CDAD− patients on antibiotic and HCW; 𝛽^on_𝑈+= probability of colonization per contact between uncolonized CDAD+ patient on antibiotic and contaminated HCW; 𝛼^on_𝑈−= average number of contacts between uncolonized CDAD+ patients on antibiotic and HCW; 𝛽^on_𝑈−= probability of colonization per contact between uncolonized CDAD− patient on antibiotic and contaminated HCW; 𝜂 = hand washing compliance factor between 0 and 1; 𝛿^off_𝐶+= CDAD+, colonized, off antibiotic: transit to CDAD−; 𝜔^on_𝐶−= CDAD−, colonized, on antibiotic: transit to CDAD+; 𝛿^on_𝐶+ = CDAD+, colonized, on antibiotic: transit to CDAD−; 𝜆^off_𝐶−= CDAD−, colonized, off antibiotic: admission rate; 𝜏^stop_𝐶−= CDAD−, colonized, on antibiotic: stop antibiotic; 𝜆^on_𝐶−= CDAD−, colonized, on antibiotic: admission rate; 𝜏^start_𝐶−= CDAD−, colonized, off antibiotic: start antibiotic; 𝛾^on_𝐶−= CDAD−, colonized, on antibiotic: average length of stay; 𝛾^off_𝐶−= CDAD−, colonized, off antibiotic: average length of stay.