Magnitude Of R0 Research Articles

Spatial panorama of malaria prevalence in Africa under climate change and interventions scenarios

BackgroundMalaria is highly sensitive to climatic variables and is strongly influenced by the presence of vectors in a region that further contribute to parasite development and sustained disease transmission. Mathematical analysis of malaria transmission through the use and application of the value of the basic reproduction number (R0) threshold is an important and useful tool for the understanding of disease patterns.MethodsTemperature dependence aspect of R0 obtained from dynamical mathematical network model was used to derive the spatial distribution maps for malaria transmission under different climatic and intervention scenarios. Model validation was conducted using MARA map and the Annual Plasmodium falciparum Entomological Inoculation Rates for Africa.ResultsThe inclusion of the coupling between patches in dynamical model seems to have no effects on the estimate of the optimal temperature (about 25 °C) for malaria transmission. In patches environment, we were able to establish a threshold value (about α = 5) representing the ratio between the migration rates from one patch to another that has no effect on the magnitude of R0. Such findings allow us to limit the production of the spatial distribution map of R0 to a single patch model. Future projections using temperature changes indicated a shift in malaria transmission areas towards the southern and northern areas of Africa and the application of the interventions scenario yielded a considerable reduction in transmission within malaria endemic areas of the continent.ConclusionsThe approach employed here is a sole study that defined the limits of contemporary malaria transmission, using R0 derived from a dynamical mathematical model. It has offered a unique prospect for measuring the impacts of interventions through simple manipulation of model parameters. Projections at scale provide options to visualize and query the results, when linked to the human population could potentially deliver adequate highlight on the number of individuals at risk of malaria infection across Africa. The findings provide a reasonable basis for understanding the fundamental effects of malaria control and could contribute towards disease elimination, which is considered as a challenge especially in the context of climate change.

The threshold of a stochastic SIQS epidemic model

Abstract In this paper, we discuss the dynamics of a stochastic SIQS epidemic model. When the noise is large, the infective decays exponentially to zero regardless of the magnitude of R 0 . When the noise is small, sufficient conditions for extinction exponentially and persistence in the mean are established. The results are illustrated by computer simulations. MSC:34F05, 37H10, 60H10, 92D25, 92D30.

Further Developments in Rapidly Decelerating Turbulent Pipe Flow Modeling

In the last two decades, energy dissipation in unsteady-state pressurized pipe flow has been examined by various authors, where the instantaneous wall shear stress is split into a quasi-steady and an unsteady shear stress component. The focus of most past studies is on formulating expressions for the unsteady wall shear stress, but there has been less work on the key parameters governing the dominance of unsteady friction in transient flows. This paper derives an expression for the head envelope damping for turbulent flows in smooth and rough pipes and provides new and carefully measured field data for the initial (i.e., pretransient) Reynolds number, R0, that ranges from 97,000 to 380,000. The analytical solutions is derived on the basis of one-dimensional (1D) water hammer equations in which the unsteady component is represented by existing convolutional unsteady friction formulas for both smooth and rough turbulent subregimes. The analytical solution is used to formulate general, encompassing and theoretically-based dimensionless parameters to assess the importance of unsteady friction in comparison to the quasi-steady component. In addition, the analytical solution furnishes the similitude relations that allowed the damping behavior from existing laboratory tests, the field tests conducted as part of this research, and the weighting function-based (WFB) models to be investigated and compared in a coherent manner in a single graph. The analysis confirms that the magnitude of R0 has a significant impact on the damping for transients generated by flow stoppage. In addition, the results show that convolutional unsteady friction model that uses the frozen eddy viscosity hypothesis and R0 has accuracy that decreases with time. An improvement for this shortcoming is proposed and verified and involves the use of the instantaneous Reynolds number in lieu of the pretransient Reynolds number in the evaluation of the WFB models. The result is a modified unsteady friction model that provides improved matches for both laboratory and field data compared with the original model.

Global Dynamics of an HTLV-1 Model with Cell-to-Cell Infection and Mitosis

A mathematical model of human T-cell lymphotropic virus type 1 in vivo with cell-to-cell infection and mitosis is formulated and studied. The basic reproductive numberR0is derived. It is proved that the dynamics of the model can be determined completely by the magnitude ofR0. The infection-free equilibrium is globally asymptotically stable (unstable) ifR0<1 (R0>1). There exists a chronic infection equilibrium and it is globally asymptotically stable ifR0>1.

Dynamics of a Multigroup SIR Epidemic Model with Nonlinear Incidence and Stochastic Perturbation

We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) ifℛ0≤1and there exists an invariant distribution which is ergodic ifℛ0>1. This is the same situation as the corresponding deterministic case. When the intensity of white noise is large, white noise controls this system. This means that the disease will extinct exponentially regardless of the magnitude ofℛ0.

Sheep Movement Networks and the Transmission of Infectious Diseases

Background and MethodologyVarious approaches have been used to investigate how properties of farm contact networks impact on the transmission of infectious diseases. The potential for transmission of an infection through a contact network can be evaluated in terms of the basic reproduction number, R 0. The magnitude of R 0 is related to the mean contact rate of a host, in this case a farm, and is further influenced by heterogeneities in contact rates of individual hosts. The latter can be evaluated as the second order moments of the contact matrix (variances in contact rates, and co-variance between contacts to and from individual hosts). Here we calculate these quantities for the farms in a country-wide livestock network: >15,000 Scottish sheep farms in each of 4 years from July 2003 to June 2007. The analysis is relevant to endemic and chronic infections with prolonged periods of infectivity of affected animals, and uses different weightings of contacts to address disease scenarios of low, intermediate and high animal-level prevalence.Principal Findings and ConclusionsAnalysis of networks of Scottish farms via sheep movements from July 2003 to June 2007 suggests that heterogeneities in movement patterns (variances and covariances of rates of movement on and off the farms) make a substantial contribution to the potential for the transmission of infectious diseases, quantified as R 0, within the farm population. A small percentage of farms (<20%) contribute the bulk of the transmission potential (>80%) and these farms could be efficiently targeted by interventions aimed at reducing spread of diseases via animal movement.

Vancomycin-resistant enterococci in intensive-care hospital settings: transmission dynamics, persistence, and the impact of infection control programs.

Vancomycin-resistant enterococci (VRE) recently have emerged as a nosocomial pathogen especially in intensive-care units (ICUs) worldwide. Transmission via the hands of health-care workers is an important determinant of spread and persistence in a VRE-endemic ICU. We describe the transmission of nosocomial pathogens by using a micro-epidemiological framework based on the transmission dynamics of vector-borne diseases. By using the concept of a basic reproductive number, R0, defined as the average number of secondary cases generated by one primary case, we show quantitatively how infection control measures such as hand washing, cohorting, and antibiotic restriction affect nosocomial cross-transmission. By using detailed molecular epidemiological surveillance and compliance monitoring, we found that the estimated basic reproductive number for VRE during a study at the Cook County Hospital, Chicago, was approximately 3-4 without infection control and 0.7 when infection control measures were included. The impact of infection control was to reduce the prevalence from a predicted 79% to an observed 36%. Hand washing and staff cohorting are the most powerful control measures although their efficacy depends on the magnitude of R0. Under the circumstances tested, endemicity of VRE was stabilized despite infection control measures, by the constant introduction of colonized patients. Multiple stochastic simulations of the model revealed excellent agreement with observed pattern. In conjunction with detailed microbiological surveillance, a mathematical framework provides a precise template to describe the colonization dynamics of VRE in ICUs and impact of infection control measures. Our analyses suggest that compliance for hand washing significantly in excess of reported levels, or the cohorting of nursing staff, are needed to prevent nosocomial transmission of VRE in endemic settings.

Repulsive Gravitation in the Kerr-Newman Field

It is shown that uncharged test particles, released from rest at infinity in the Kerr-Newman field, stop and rebound when the radial coordinate r takes the value r0 = Q2/(2M). This expression corresponds to the position of a stationary source of the Kerr-Newman field found by the author. It represents the surface of a massive oblate ellipsoid of revolution undergoing rigid rotation. Besides, the magnitude of r0 guarantees that no violation of causality occurs throughout spacetime. Although the test particles' angular momenta are always zero, they acquire a rotational motion as a consequence of the dragging of inertial frames.

The estimation of the basic reproduction number for infectious diseases.

The basic reproduction number R0 is the number of secondary cases which one case would produce in a completely susceptible population. It depends on the duration of the infectious period, the probability of infecting a susceptible individual during one contact, and the number of new susceptible individuals contacted per unit of time. Therefore R0 may vary considerably for different infectious diseases but also for the same disease in different populations. The key threshold result of epidemic theory associates the outbreaks of epidemics and the persistence of endemic levels with basic reproduction numbers greater than one. Because the magnitude of R0 allows one to determine the amount of effort which is necessary either to prevent an epidemic or to eliminate an infection from a population, it is crucial to estimate R0 for a given disease in a particular population. The present paper gives a survey about the various estimation methods available.