DETERMINISTIC AND STOCHASTIC MODELING OF NOSOCOMIAL INFECTION TRANSMISSION INCORPORATING PATIENTS’ FAMILY CAREGIVERS AS TRANSMISSION VECTORS
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Abstract
Nosocomial infections, also known as hospital-acquired infections, are bacterial infections contracted within healthcare settings. They contribute significantly to the burden of disease by prolonging hospital stays, increasing treatment costs, complicating surgical outcomes, and, in severe cases, leading to death. Methicillin resistant staphylococcus aureus (MRSA) is the most isolated
pathogen of nosocomial infections and the most studied in the literature. Despite their impact, awareness of nosocomial infections remains limited, leaving patients, healthcare workers, visitors, and even family caregivers vulnerable to its transmission. In low-income and middle-income countries the practice of a family caregiver assisting an inpatient is common, and they can contact and transmit infections while carrying out various activities within the hospital environment. Deterministic and stochastic models have been widely applied to understand the transmission dynamics of nosocomial infections and provide valuable insights. However, existing models have often overlooked the role of patients’ family caregivers, who can act as important but underrecognized vectors of transmission. In this thesis, deterministic and stochastic models that explicitly incorporate family caregivers as a distinct transmission pathway of methicillin-resistant Staphylococcus aureus (MRSA) are developed. For the deterministic framework, the basic reproduction number �0 is derived along with the conditions for disease-free and endemic equilibria. The stochastic framework developed using a Continuous-time Markov Chain (CTMC) extends the deterministic model by incorporating random fluctuations through its drift and diffusion terms. This provides deeper insight into the system’s variability, extinction probabilities, and outbreak risks that cannot be fully captured by the deterministic model. For the deterministic model, the basic reproduction number is evaluated and subjected to sensitivity analysis, using plausible parameter values from surveillance studies within Nigerian hospitals, whereby revealing the dominant influence of hand-hygiene compliance of caregivers and healthcare workers, as well as decontamination rates of both caregivers and healthcare workers. The stochastic simulation in MATLAB gives the stochastic sample paths, time-series behaviours of the state variables and extinction probability. The numerical results illustrate that while the deterministic model captures mean epidemic behaviours, stochastic models reveal substantial variability and probability of infection extinction especially in settings with effective hand hygiene compliance of caregivers and healthcare workers. These analyses reveal the importance of integrating patients’ family caregivers in modeling the spread of MRSA in hospitals.
pathogen of nosocomial infections and the most studied in the literature. Despite their impact, awareness of nosocomial infections remains limited, leaving patients, healthcare workers, visitors, and even family caregivers vulnerable to its transmission. In low-income and middle-income countries the practice of a family caregiver assisting an inpatient is common, and they can contact and transmit infections while carrying out various activities within the hospital environment. Deterministic and stochastic models have been widely applied to understand the transmission dynamics of nosocomial infections and provide valuable insights. However, existing models have often overlooked the role of patients’ family caregivers, who can act as important but underrecognized vectors of transmission. In this thesis, deterministic and stochastic models that explicitly incorporate family caregivers as a distinct transmission pathway of methicillin-resistant Staphylococcus aureus (MRSA) are developed. For the deterministic framework, the basic reproduction number �0 is derived along with the conditions for disease-free and endemic equilibria. The stochastic framework developed using a Continuous-time Markov Chain (CTMC) extends the deterministic model by incorporating random fluctuations through its drift and diffusion terms. This provides deeper insight into the system’s variability, extinction probabilities, and outbreak risks that cannot be fully captured by the deterministic model. For the deterministic model, the basic reproduction number is evaluated and subjected to sensitivity analysis, using plausible parameter values from surveillance studies within Nigerian hospitals, whereby revealing the dominant influence of hand-hygiene compliance of caregivers and healthcare workers, as well as decontamination rates of both caregivers and healthcare workers. The stochastic simulation in MATLAB gives the stochastic sample paths, time-series behaviours of the state variables and extinction probability. The numerical results illustrate that while the deterministic model captures mean epidemic behaviours, stochastic models reveal substantial variability and probability of infection extinction especially in settings with effective hand hygiene compliance of caregivers and healthcare workers. These analyses reveal the importance of integrating patients’ family caregivers in modeling the spread of MRSA in hospitals.
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