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Basic reproductive number

Clara Champagne, David Georges Salthouse, Richard Paul, Van-Mai Cao-Lormeau, Benjamin Roche, Bernard Cazelles
Before the outbreak that reached the Americas in 2015, Zika virus (ZIKV) circulated in Asia and the Pacific: these past epidemics can be highly informative on the key parameters driving virus transmission, such as the basic reproduction number (R0). We compare two compartmental models with different mosquito representations, using surveillance and seroprevalence data for several ZIKV outbreaks in Pacific islands (Yap, Micronesia 2007, Tahiti and Moorea, French Polynesia 2013-2014, New Caledonia 2014). Models are estimated in a stochastic framework with recent Bayesian techniques...
November 29, 2016: ELife
Najat Ziyadi
We introduce mathematical human papillomavirus (HPV) epidemic models (with and without vaccination) for African American females (AAF) and African American males (AAM) with ''fitted'' logistic demographics and use these models to study the HPV disease dynamics. The US Census Bureau data of AAF and AAM of 16 years and older from 2000 to 2014 is used to ''fit'' the logistic demographic models. We compute the basic reproduction number, R0, and use it to show that R0 is less than 1 in the African American (AA) population with or without implementation of HPV vaccination program...
February 1, 2017: Mathematical Biosciences and Engineering: MBE
Kazuo Yamazaki, Xueying Wang
We study the global stability issue of the reaction-convection-diffusion cholera epidemic PDE model and show that the basic reproduction number serves as a threshold parameter that predicts whether cholera will persist or become globally extinct. Specifically, when the basic reproduction number is beneath one, we show that the disease-free-equilibrium is globally attractive. On the other hand, when the basic reproduction number exceeds one, if the infectious hosts or the concentration of bacteria in the contaminated water are not initially identically zero, we prove the uniform persistence result and that there exists at least one positive steady state...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Kazeem Oare Okosun, Robert Smith
This paper presents a mathematical model for malaria--schistosomiasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria...
April 1, 2017: Mathematical Biosciences and Engineering: MBE
Priscila Ariane Auler, Letícia Carvalho Benitez, Marcelo Nogueira do Amaral, Isabel Lopes Vighi, Gabriela Dos Santos Rodrigues, Luciano Carlos da Maia, Eugenia Jacira Bolacel Braga
Many studies use strategies that allow for the identification of a large number of genes expressed in response to different stress conditions to which the plant is subjected throughout its cycle. In order to obtain accurate and reliable results in gene expression studies, it is necessary to use reference genes, which must have uniform expression in the majority of cells in the organism studied. RNA isolation of leaves and expression analysis in real-time quantitative polymerase chain reaction (RT-qPCR) were carried out...
November 23, 2016: Journal of Applied Genetics
Pengwei Lou, Lei Wang, Xueliang Zhang, Jiabo Xu, Kai Wang
Brucellosis is one of the severe public health problems; the cumulative number of new human brucellosis cases reached 211515 from 2010 to 2014 in China. Bayingolin Mongol Autonomous Prefecture is situated in the southeast of Xinjiang, where brucellosis infection occurs every year. Based on the reported data of newly acute human brucellosis cases for each season in Bayingolin Mongol Autonomous Prefecture, we proposed a susceptible, exposed, infected, and vaccinated (SEIV) model with periodic transmission rates to investigate the seasonal brucellosis transmission dynamics among sheep/cattle and from sheep/cattle to humans...
2016: BioMed Research International
Jijun Zhao, Fachun Jiang, Lianfa Zhong, Jianping Sun, Junhang Ding
BACKGROUND: Hand, foot and mouth disease (HFMD) has circulated in China and caused yearly outbreak. To understand the transmission of the disease and to assess the spatial variation in cases reported, we examined age-specific transmission characteristics and reporting rates of HFMD for 31 provinces in mainland China. METHODS: We first analyzed incidence spatial patterns and age-specific incidence patterns using dataset from 2008 to 2012. Transmission characteristics were estimated based on catalytic model...
November 21, 2016: BMC Infectious Diseases
Tahir Khan, Gul Zaman, M Ikhlaq Chohan
In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number [Formula: see text]. We show that if [Formula: see text] then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if [Formula: see text]...
December 2017: Journal of Biological Dynamics
Sherry Towers, Fred Brauer, Carlos Castillo-Chavez, Andrew K I Falconar, Anuj Mubayi, Claudia M E Romero-Vivas
BACKGROUND: In 2015, the Zika arbovirus (ZIKV) began circulating in the Americas, rapidly expanding its global geographic range in explosive outbreaks. Unusual among mosquito-borne diseases, ZIKV has been shown to also be sexually transmitted, although sustained autochthonous transmission due to sexual transmission alone has not been observed, indicating the reproduction number (R0) for sexual transmission alone is less than 1. Critical to the assessment of outbreak risk, estimation of the potential attack rates, and assessment of control measures, are estimates of the basic reproduction number, R0...
October 17, 2016: Epidemics
Ke Li, Kalyanmoy Deb, Qingfu Zhang, Qiang Zhang
Nondominated sorting (NDS), which divides a population into several nondomination levels (NDLs), is a basic step in many evolutionary multiobjective optimization (EMO) algorithms. It has been widely studied in a generational evolution model, where the environmental selection is performed after generating a whole population of offspring. However, in a steady-state evolution model, where a population is updated right after the generation of a new candidate, the NDS can be extremely time consuming. This is especially severe when the number of objectives and population size become large...
November 8, 2016: IEEE Transactions on Cybernetics
F B Agusto
The Ebola virus disease is caused by the Ebola virus which belongs to the filoviridae virus family. The 2014 outbreaks were estimated to have caused over 11,000 fatalities. In this paper, we formulate and analyze a system of ordinary differential equations which incorporates disease relapse and reinfection. The Ebola model with disease relapse and reinfection is locally-asymptotically stable when the basic reproduction number is less than unity. The model exhibits in the presence of disease reinfection, the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity...
November 8, 2016: Mathematical Biosciences
Mayumbo Nyirenda, Ryosuke Omori, Heidi L Tessmer, Hiroki Arimura, Kimihito Ito
The prediction of the lineage dynamics of influenza B viruses for the next season is one of the largest obstacles for constructing an appropriate influenza trivalent vaccine. Seasonal fluctuation of transmissibility and epidemiological interference between the two major influenza B lineages make the lineage dynamics complicated. Here we construct a parsimonious model describing the lineage dynamics while taking into account seasonal fluctuation of transmissibility and epidemiological interference. Using this model we estimated the epidemiological and evolutional parameters with the time-series data of the lineage specific isolates in Japan from the 2010-2011 season to the 2014-2015 season...
2016: PloS One
Christie Mayo, Courtney Shelley, N James MacLachlan, Ian Gardner, David Hartley, Christopher Barker
The global distribution of bluetongue virus (BTV) has been changing recently, perhaps as a result of climate change. To evaluate the risk of BTV infection and transmission in a BTV-endemic region of California, sentinel dairy cows were evaluated for BTV infection, and populations of Culicoides vectors were collected at different sites using carbon dioxide. A deterministic model was developed to quantify risk and guide future mitigation strategies to reduce BTV infection in California dairy cattle. The greatest risk of BTV transmission was predicted within the warm Central Valley of California that contains the highest density of dairy cattle in the United States...
2016: PloS One
Tom Britton, David Juher, Joan Saldaña
This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate [Formula: see text] (and reconnect to non-infectious individuals with probability [Formula: see text] or else simply drop the edge if [Formula: see text]), so-called preventive rewiring. The models are denoted SIR-[Formula: see text] and SEIR-[Formula: see text], and we focus attention on the early stages of an outbreak, where we derive the expressions for the basic reproduction number [Formula: see text] and the expected degree of the infectious nodes [Formula: see text] using two different approximation approaches...
October 31, 2016: Bulletin of Mathematical Biology
Zhengqing Zhang, Huapeng Wang, Chunfeng Hao, Wei Zhang, Miaomiao Yang, Yong Chang, Menglou Li
Dastarcus helophoroides, which has a relatively longer lifespan compared to other insects, is one of the most effective natural enemies of many large-body long-horned beetles. Methuselah (Mth) is associated with the lifespan, stress resistance, and reproduction in Drosophila melanogaster, but Mth is not present in non-drosophiline insects. A number of methuselah-like genes (mth-likes, mthls) have been identified in non-drosophiline insects, but it is still unknown whether they are present in Dastarcus helophoroides...
October 21, 2016: Genes
Andreas Widder, Christian Kuehn
In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical reformulation of the basic reproduction number, the homogeneous system and the heterogeneous system exhibit a completely analogous global behaviour. Then we consider noise terms to incorporate the fluctuation effects and the random import of the disease into the population and analyse the influence of heterogeneity on warning signs for critical transitions (or tipping points)...
October 1, 2016: Mathematical Biosciences and Engineering: MBE
Oscar Patterson-Lomba, Muntaser Safan, Sherry Towers, Jay Taylor
Urban areas, with large and dense populations, offer conditions that favor the emergence and spread of certain infectious diseases. One common feature of urban populations is the existence of large socioeconomic inequalities which are often mirrored by disparities in access to healthcare. Recent empirical evidence suggests that higher levels of socioeconomic inequalities are associated with worsened public health outcomes, including higher rates of sexually transmitted diseases (STD's) and lower life expectancy...
October 1, 2016: Mathematical Biosciences and Engineering: MBE
Jianquan Li, Yiqun Li, Yali Yang
The epidemic characteristics, including the epidemic final size, peak, and turning point, of two classical SIR models with disease-induced death are investigated when a small initial value of the infective population is released. The models have mass-action (i.e. bilinear), or density dependent (i.e. standard) incidence, respectively. For the two models, the conditions that determining whether the related epidemic characteristics of an epidemic outbreak appear are explicitly determine by rigorous mathematical analysis...
October 1, 2016: Mathematical Biosciences and Engineering: MBE
Ali Gharouni, Lin Wang
A patch-structured multigroup-like $SIS$ epidemiological model is proposed to study the spread of the common bed bug infestation. It is shown that the model exhibits global threshold dynamics with the basic reproduction number as the threshold parameter. Costs associated with the disinfestation process are incorporated into setting up the optimization problems. Procedures are proposed and simulated for finding optimal resource allocation strategies to achieve the infestation free state. Our analysis and simulations provide useful insights on how to efficiently distribute the available exterminators among the infested patches for optimal disinfestation management...
October 1, 2016: Mathematical Biosciences and Engineering: MBE
Xichao Duan, Sanling Yuan, Kaifa Wang
In this paper, we propose and investigate an age-structured hepatitis B virus (HBV) model with saturating incidence and spatial diffusion where the viral contamination process is described by the age-since-infection. We first analyze the well-posedness of the initial-boundary values problem of the model in the bounded domain Ω ⊂ Rn and obtain an explicit formula for the basic reproductive number R0 of the model. Then we investigate the global behavior of the model in terms of R0: if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable, whereas if R0 > 1, then the infected steady state is globally asymptotically stable...
October 1, 2016: Mathematical Biosciences and Engineering: MBE
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