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Basic reproductive number

Soyoung Kim, Jonggul Lee, Eunok Jung
A mathematical model for the transmission dynamics of the 2009 A/H1N1 influenza epidemic in the Republic of Korea is developed. The simulation period is separated into three consecutive periods based on the government's intervention strategies: the nonpharmaceutical strategy is used during Period 1. The nonpharmaceutical and antiviral strategies are executed during Period 2 and the vaccine strategy is added during Period 3. During Period 1, we estimate the reduction in the transmission rate due to the government's intervention policies as a difference between the data-fitted and uncontrolled transmission rate that is derived from the basic reproductive number, R0, of the model without intervention...
October 18, 2016: Journal of Theoretical Biology
Xia Wang, Sanyi Tang, Xinyu Song, Libin Rong
HIV can infect cells via virus-to-cell infection or cell-to-cell viral transmission. These two infection modes may occur in a synergistic way and facilitate viral spread within an infected individual. In this paper, we developed an HIV latent infection model including both modes of transmission and time delays between viral entry and integration or viral production. We analysed the model by defining the basic reproductive number, showing the existence, positivity and boundedness of the solution, and proving the local and global stability of the infection-free and infected steady states...
October 12, 2016: Journal of Biological Dynamics
Kolade M Owolabi
Evolution systems containing fractional derivatives can result to suitable mathematical models for describing better and important physical phenomena. In this paper, we consider a multi-components nonlinear fractional-in-space reaction-diffusion equations consisting of an improved deterministic model which describe the spread of hepatitis B virus disease in areas of high endemic communities. The model is analyzed. We give some useful biological results to show that the disease-free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity...
2016: SpringerPlus
Julia Reis, Jeffrey Shaman
Recent studies have shown that systems combining mathematical modeling and Bayesian inference methods can be used to generate real-time forecasts of future infectious disease incidence. Here we develop such a system to study and forecast respiratory syncytial virus (RSV). RSV is the most common cause of acute lower respiratory infection and bronchiolitis. Advanced warning of the epidemic timing and volume of RSV patient surges has the potential to reduce well-documented delays of treatment in emergency departments...
October 2016: PLoS Computational Biology
Zachary S Brown, Randall A Kramer, David Ocan, Christine Oryema
BACKGROUND: Insecticide-based tools remain critical for controlling vector-borne diseases in Uganda. Securing public support from targeted populations for such tools is an important component in sustaining their long-run effectiveness. Yet little quantitative evidence is available on the perceived benefits and costs of vector control programmes among targeted households. METHODS: A survey was administered to a clustered random sample of 612 households in Gulu and Oyam districts of northern Uganda during a period of very high malaria transmission and following a pilot indoor residual spray (IRS) programme...
October 6, 2016: Infectious Diseases of Poverty
Qili Fei, Li Yang, Wanqi Liang, Dabing Zhang, Blake C Meyers
Dissection of the genetic pathways and mechanisms by which anther development occurs in grasses is crucial for both a basic understanding of plant development and for examining traits of agronomic importance such as male sterility. In rice, MULTIPLE SPOROCYTES1 (MSP1), a leucine-rich-repeat receptor kinase, plays an important role in anther development by limiting the number of sporocytes. OsTDL1a (a TPD1-like gene in rice) encodes a small protein that acts as a cofactor of MSP1 in the same regulatory pathway...
October 4, 2016: Journal of Experimental Botany
A De, K Maity, Soovoojeet Jana, M Maiti
Japanese encephalitis (JE) is a public health problem that threats the entire world today. Japanese Encephalitis virus (JEV) mostly became a threat due to the significant number of increase of susceptible mosquito vectors and vertebrate hosts in Asia by which around 70,000 cases and 10,000 deaths per year took place in children below 15 years of age. In this paper, a mathematical model of JE due to JEV from the vector source (infected mosquito) and two vertebrate hosts (infected human and infected pig) is formulated...
October 1, 2016: Mathematical Biosciences
A Ulloa-Aguirre, S Lira-Albarrán
The pituitary gonadotropins, luteinizing hormone (LH), and follicle-stimulating hormone (FSH) play a pivotal role in reproduction. The synthesis and secretion of gonadotropins are regulated by complex interactions among several endocrine, paracrine, and autocrine factors of diverse chemical structure. In men, LH regulates the synthesis of androgens by the Leydig cells, whereas FSH promotes Sertoli cell function and thereby influences spermatogenesis. Gonadotropins are complex molecules composed of two subunits, the α- and β-subunit, that are noncovalently associated...
2016: Progress in Molecular Biology and Translational Science
Walter J Tabachnick
Mosquitoes transmit many viruses to a variety of hosts. Cycles of mosquito borne arbovirus transmission are the result of complex interactions between the mosquito, the arbovirus and the host that are influenced by genetic variations in a variety of traits in each that are all influenced by many environmental factors. R0, the basic reproduction number or mean number of individuals infected from a single infected individual, is a measure of mosquito borne arbovirus transmission. Understanding the causes for the distribution of R0 in any transmission cycle is a daunting challenge due to the lack of information on the genetic and environmental variances that influence R0...
September 28, 2016: Current Opinion in Virology
Nataliya G Batina, Christopher J Crnich, David F Anderson, Dörte Döpfer
BACKGROUND: Residents of nursing homes are commonly colonized with methicillin-resistant Staphylococcus aureus (MRSA) but there is a limited understanding of the dynamics and determinants of spread in this setting. To address this gap, we sought to use mathematical modeling to assess the epidemic potential of MRSA in nursing homes and to determine conditions under which non-USA300 and USA300 MRSA could be eliminated or reduced in the facilities. METHODS: Model parameters were estimated from data generated during a longitudinal study of MRSA in 6 Wisconsin nursing homes...
2016: Antimicrobial Resistance and Infection Control
N J Malunguza, S D Hove-Musekwa, S Dube, Z Mukandavire
Super-infection by multiple HIV-1 subtypes, previously thought restricted to high risk groups, has now been reported in the general heterosexual populations at relatively the same incidence rate as in high risk groups. We present a simple deterministic HIV model with super-infection by two HIV-1 subtypes. Mathematical characteristics including the basic reproductive number [Formula: see text], invasion threshold [Formula: see text] and conditions for asymptotic stability are derived. In the absence of super-infection the model exhibits competitive exclusion, and all equilibria are globally attracting if they exist except for the disease free which is a saddle for [Formula: see text] The results show that the subtype with the dominant reproductive number exceeding unity dominates the weaker subtype forcing it to extinction regardless of the size of the reproductive number...
September 25, 2016: Mathematical Medicine and Biology: a Journal of the IMA
Karl Peter Hadeler, Klaus Dietz, Muntaser Safan
The asymptotically homogeneous SIR model of Thieme (1992) for growing populations, with incidence depending in a general way on total population size, is reconsidered with respect to other parameterizations that give clear insight into epidemiological relevant relations and thresholds. One important feature of the present approach is case fatality as opposed to differential mortality. Although case fatality models and differential mortality models are equivalent via a transformation in parameter space, the underlying ideas and the dynamic behaviors are different, e...
November 2016: Mathematical Biosciences
Daozhou Gao, Travis C Porco, Shigui Ruan
A susceptible-infectious-susceptible (SIS) epidemic model that describes the coinfection and cotransmission of two infectious diseases spreading through a single population is studied. The host population consists of two subclasses: susceptible and infectious, and the infectious individuals are further divided into three subgroups: those infected by the first agent/pathogen, the second agent/pathogen, and both. The basic reproduction numbers for all cases are derived which completely determine the global stability of the system if the presence of one agent/pathogen does not affect the transmission of the other...
October 1, 2016: Journal of Mathematical Analysis and Applications
F I Korennoy, V M Gulenkin, A E Gogin, T Vergne, A K Karaulov
In 1977, Ukraine experienced a local epidemic of African swine fever (ASF) in the Odessa region. A total of 20 settlements were affected during the course of the epidemic, including both large farms and backyard households. Thanks to timely interventions, the virus circulation was successfully eradicated within 6 months, leading to no additional outbreaks. Detailed report of the outbreak's investigation has been publically available from 2014. The report contains some quantitative data that allow studying the ASF-spread dynamics in the course of the epidemic...
September 25, 2016: Transboundary and Emerging Diseases
Li-Ming Cai, Xue-Zhi Li, Bin Fang, Shigui Ruan
Since there exist extrinsic and intrinsic incubation periods of pathogens in the feedback interactions between the vectors and hosts, it is necessary to consider the incubation delays in vector-host disease transmission dynamics. In this paper, we propose vector-host disease models with two time delays, one describing the incubation period in the vector population and another representing the incubation period in the host population. Both distributed and discrete delays are used. By constructing suitable Liapunov functions, we obtain sufficient conditions for the global stability of the endemic equilibria of these models...
September 22, 2016: Journal of Mathematical Biology
Biao Tang, Yanni Xiao, Sanyi Tang, Jianhong Wu
We develop a mathematical model to closely mimic the integrated program of impulsive vector control (every Friday afternoon since the initiation of the program) and continuous patient treatment and isolation implemented in the Guangdong Province of China during its 2014 dengue outbreak. We fitted the data of accumulated infections and used the parameterized model to carry out a retrospective analysis to estimate the basic reproduction number 1.7425 (95% CI 1.4443-2.0408), the control reproduction number 0.1709, and the mosquito-killing ratios 0...
September 17, 2016: Journal of Theoretical Biology
Eric Foxall, Nicolas Lanchier
We consider a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in each patch at a rate proportional to the number of pairs of individuals in the patch (sexual reproduction) rather than simply the number of individuals as in the basic contact process. Offspring produced at a given patch either stay in their parents' patch or are sent to a nearby patch with some fixed probabilities...
September 19, 2016: Journal of Mathematical Biology
Mengfeng Sun, Haifeng Zhang, Huiyan Kang, Guanghu Zhu, Xinchu Fu
We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation...
September 17, 2016: Journal of Mathematical Biology
Frank Wen, Trevor Bedford, Sarah Cobey
Most antigenically novel and evolutionarily successful strains of seasonal influenza A (H3N2) originate in East, South and Southeast Asia. To understand this pattern, we simulated the ecological and evolutionary dynamics of influenza in a host metapopulation representing the temperate north, tropics and temperate south. Although seasonality and air traffic are frequently used to explain global migratory patterns of influenza, we find that other factors may have a comparable or greater impact. Notably, a region's basic reproductive number (R0) strongly affects the antigenic evolution of its viral population and the probability that its strains will spread and fix globally: a 17-28% higher R0 in one region can explain the observed patterns...
September 14, 2016: Proceedings. Biological Sciences
Ling Xue, Carrie A Manore, Panpim Thongsripong, James M Hyman
We develop and analyse an ordinary differential equation model to investigate the transmission dynamics of releasing Wolbachia-infected mosquitoes to establish an endemic infection in a population of wild uninfected mosquitoes. Wolbachia is a genus of endosymbiotic bacteria that can infect mosquitoes and reduce their ability to transmit some viral mosquito-transmitted diseases, including dengue fever, chikungunya, and Zika. Although the bacterium is transmitted vertically from infected mothers to their offspring, it can be difficult to establish an endemic infection in a wild mosquito population...
September 14, 2016: Journal of Biological Dynamics
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