Effects of the proportion of high-risk patients and control strategies on the prevalence of methicillin-resistant Staphylococcus aureus in an intensive care unit.

BACKGROUND: The presence of nosocomial pathogens in many intensive care units poses a threat to patients and public health worldwide. Methicillin-resistant Staphylococcus aureus (MRSA) is an important pathogen endemic in many hospital settings. Patients who are colonized with MRSA may develop an infection that can complicate their prior illness. METHODS: A mathematical model to describe transmission dynamics of MRSA among high-risk and low-risk patients in an intensive care unit (ICU) via hands of health care workers is developed. We aim to explore the effects of the proportion of high-risk patients, the admission proportions of colonized and infected patients, the probability of developing an MRSA infection, and control strategies on MRSA prevalence among patients. RESULTS: The increasing proportion of colonized and infected patients at admission, along with the higher proportion of high-risk patients in an ICU, may significantly increase MRSA prevalence. In addition, the prevalence becomes higher if patients in the high-risk group are more likely to develop an MRSA infection. Our results also suggest that additional infection prevention and control measures targeting high-risk patients may considerably help reduce MRSA prevalence as compared to those targeting low-risk patients. CONCLUSIONS: The proportion of high-risk patients and the proportion of colonized and infected patients in the high-risk group at admission may play an important role on MRSA prevalence. Control strategies targeting high-risk patients may help reduce MRSA prevalence.

Modeling Clostridium difficile in a hospital setting: control and admissions of colonized and symptomatic patients.

BACKGROUND: Clostridium difficile (C. difficile) infection is an important cause of healthcare-associated diarrhea. Several factors such as admission of colonized patients, levels of serum antibodies in patients, and control strategies may involve in determining the prevalence and the persistence of C. difficile in a hospital unit. METHODS: We develop mathematical models based on deterministic and stochastic frameworks to investigate the effects of control strategies for colonized and symptomatic patients and admissions of colonized and symptomatic patients on the prevalence and the persistence of C. difficile. RESULTS: Our findings suggest that control strategies and admissions of colonized and symptomatic patients play important roles in determining the prevalence and the persistence of C. difficile. Improving control of C. difficile in colonized and symptomatic patients may generally help reduce the prevalence and the persistence of C. difficile. However, if admission rates of colonized and symptomatic patients are high, the prevalence of C. difficile may remain high in a patient population even though strict control policies are applied. CONCLUSION: Control strategies and admissions of colonized and symptomatic patients are important determinants of the prevalence and the persistence of C. difficile.

Modeling the spread of capripoxvirus among livestock and optimal vaccination strategies.

Capripox is an important transboundary animal disease that is endemic across Africa, the Middle East, and some parts of Asia. The disease is highly contagious and considered to be a major obstacle causing significant economic loses in many agricultural areas. In this study, a mathematical model is developed to describe the transmission dynamics of capripoxvirus (CaPV) among livestock. This proposed model incorporates direct and indirect transmission of CaPV, together with two vaccination strategies, to investigate their effects on the severity of outbreaks and the prevalence of CaPV among the livestock population. The results suggest that ratio of potential vectors to livestock, successful probability of infection, vaccination rates, waning rate of vaccine-conferred protection, and virus introduction time play crucial roles in determining the outbreak severity and the prevalence level. The results also show that it is optimal to vaccinate newborns at the maximum effort throughout the control program and moderately increase vaccination rate for a susceptible pool to reach its maximum level after the outbreak.

Transmission Dynamics of Rift Valley Fever Virus: Effects of Live and Killed Vaccines on Epizootic Outbreaks and Enzootic Maintenance.

Rift Valley fever virus (RVFV) is an arthropod-borne viral pathogen that causes significant morbidity and mortality in small ruminants throughout Africa and the Middle East. Due to the sporadic and explosive nature of RVF outbreaks, vaccination has proved challenging to reduce RVFV infection in the ruminant population. Currently, there are two available types of vaccines, live and killed, in endemic areas. In this study, two mathematical models have been developed to explore the impact of live and killed vaccines on the transmission dynamics of RVFV. We demonstrate in general that vaccination helps reduce the severity of RVF outbreaks and that less delay in implementation and more vaccination attempts and effective vaccines can reduce the outbreak magnitude and the endemic number of RVFV. However, an introduction of a number of ruminants vaccinated by live vaccines in RVFV-free areas may cause an outbreak and RVFV may become endemic if there is sustained use of live vaccines. Other factors that are the important determinants of RVF outbreaks include: unsustained vaccination programs, recruitment of susceptible ruminants, and the seasonal abundance of mosquitoes.

A modeling approach to investigate epizootic outbreaks and enzootic maintenance of Rift Valley fever virus.

We propose a mathematical model to investigate the transmission dynamics of Rift Valley fever (RVF) virus among ruminants. Our findings indicate that in endemic areas RVF virus maintains at a very low level among ruminants after outbreaks and subsequent outbreaks may occur when new susceptible ruminants are recruited into endemic areas or abundant numbers of mosquitoes emerge when herd immunity decreases. Many factors have been shown to have impacts on the severity of RVF outbreaks; a higher probability of death due to RVF among ruminants, a higher mosquito:ruminant ratio, or a shorter lifespan of animals can amplify the magnitude of the outbreaks; vaccination helps to reduce the magnitude of RVF outbreaks and the loss of animals efficiently, and the maximum vaccination effort (a high vaccination rate and a larger number of vaccinated animals) is recommended before the commencement of an outbreak but can be reduced later during the enzootic.

Modeling Plasmodium vivax: relapses, treatment, seasonality, and G6PD deficiency.

Plasmodium vivax (P. vivax) is one of the most important human malaria species that is geographically widely endemic and causes social and economic burden globally. However, its consequences have long been neglected and underestimated as it has been mistakenly considered a benign and inconsequential malaria species as compared to Plasmodium falciparum. One of the important differences between P. falciparum and P. vivax is the formation of P. vivax latent-stage parasites (hypnozoites) that can cause relapses after a course of treatment. In this work, mathematical modeling is employed to investigate how patterns of incubation periods and relapses of P. vivax, variation in treatment, and seasonal abundance of mosquitoes influence the number of humans infected with P. vivax and the mean age at infection of humans in tropical and temperate regions. The model predicts that: (i) the number of humans infected with P. vivax may increase when an incubation period of parasites in humans and a latent period of hypnozoites decrease; (ii) without primaquine, the only licensed drug to prevent relapses, P. vivax may be highly prevalent; (iii) the mean age at infection of humans may increase when a latent period of hypnozoites increases; (iv) the number of infectious humans may peak at a few months before the middle of each dry season and the number of hypnozoite carriers may peak at nearly the middle of each dry season. In addition, glucose-6-phosphate-dehydrogenase (G6PD) deficiency, which is the most common enzyme defect in humans that may provide some protection against P. vivax infection and severity, is taken into account to study its impact on the number of humans infected with P. vivax. Modeling results indicate that the increased number of infected humans may result from a combination of a larger proportion of humans with G6PD deficiency in the population, a lesser protection of G6PD deficiency to P. vivax infection, and a shorter latent period of hypnozoites.

Modeling methicillin-resistant Staphylococcus aureus in hospitals: transmission dynamics, antibiotic usage and its history.

BACKGROUND: Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, posing substantial threats and economic burdens worldwide. METHODS: We propose mathematical models to investigate the transmission dynamics of MRSA and determine factors that influence the prevalence of MRSA infection when antibiotics are given to patients to treat or prevent infections with either MRSA itself or other bacterial pathogens. RESULTS: Our results suggest that: (i) MRSA always persists in the hospital when colonized and infected patients are admitted; (ii) the longer the duration of treatment of infected patients and the lower the probability of successful treatment will increase the prevalence of MRSA infection; (iii) the longer the duration of contamination of health care workers (HCWs) and the more their contacts with patients may increase the prevalence of MRSA infection; (iv) possible ways to control the prevalence of MRSA infection include treating patients with antibiotic history as quickly and efficiently as possible, screening and isolating colonized and infected patients at admission, and compliance with strict hand-washing rules by HCWs. CONCLUSION: Our modeling studies offer an approach to investigating MRSA infection in hospital settings and the impact of antibiotic history on the incidence of infection. Our findings suggest important influences on the prevalence of MRSA infection which may be useful in designing control policies.

Modeling the spread of methicillin-resistant Staphylococcus aureus in nursing homes for elderly.

Methicillin-resistant Staphylococcus aureus (MRSA) is endemic in many hospital settings, including nursing homes. It is an important nosocomial pathogen that causes mortality and an economic burden to patients, hospitals, and the community. The epidemiology of the bacteria in nursing homes is both hospital- and community-like. Transmission occurs via hands of health care workers (HCWs) and direct contacts among residents during social activities. In this work, mathematical modeling in both deterministic and stochastic frameworks is used to study dissemination of MRSA among residents and HCWs, persistence and prevalence of MRSA in a population, and possible means of controlling the spread of this pathogen in nursing homes. The model predicts that: (i) without strict screening and decolonization of colonized individuals at admission, MRSA may persist; (ii) decolonization of colonized residents, improving hand hygiene in both residents and HCWs, reducing the duration of contamination of HCWs, and decreasing the resident∶staff ratio are possible control strategies; (iii) the mean time that a resident remains susceptible since admission may be prolonged by screening and decolonization treatment in colonized individuals; (iv) in the stochastic framework, the total number of colonized residents varies and may increase when the admission of colonized residents, the duration of colonization, the average number of contacts among residents, or the average number of contacts that each resident requires from HCWs increases; (v) an introduction of a colonized individual into an MRSA-free nursing home has a much higher probability of leading to a major outbreak taking off than an introduction of a contaminated HCW.

Analysis of a vector-bias model on malaria transmission.

We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcritical bifurcation occurs at the basic reproductive ratio equalling 1 by projecting the flow onto the extended centre manifold. We next study the dynamics of the system when incubation time of malaria parasites in mosquitoes is included, and find that the longer incubation time reduces the prevalence of malaria. Also, we incorporate a random movement of mosquitoes as a diffusion term and a chemically directed movement of mosquitoes to humans expressed in terms of sweat and body odour as a chemotaxis term to study the propagation of infected population to uninfected population. We find that a travelling wave occurs; its speed is calculated numerically and estimated for the lower bound analytically.