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Topic: Basic reproduction number

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Mathematical modelling in epidemiology

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	Figures
		The distribution of A, the total number of infected persons excluding those infected contacts who were vaccinated on time to prevent disease, and B, the time to extinction for 500 simulation runs with the baseline intervention parameter values and a basic reproduction number of 5.23.
		For a basic reproduction number of 10.46 and an increase of the vaccination coverage in the casual contact ring to 80% in C, the distribution of the total number of infected persons, and in D, the distribution of the time to extinction is shown for 500 simulation runs.
		The total number of infected persons (excluding successfully vaccinated infected contacts) depends on A, the number of index cases starting the epidemic, and B, the day of the infectious period after which the diagnosis of the first case occurs.
	www.medscape.com /content/2004/00/47/48/474835/474835_fig.html (629 words)

	Mathematical modelling in epidemiology - Wikipedia, the free encyclopedia
		This article uses some basic assumptions and some simple mathematics to find parameters for various infectious diseases and to use those parameters to make useful calculations about the effects of a mass vaccination programme.
		S = the proportion of the population (given as a decimal between 0 and 1) who are susceptible to the disease (that is, not immune).
		Notice that this relation means that for a disease to be in the endemic steady state, the higher the basic reproduction number, the lower the proportion of the population susceptible must be, and vice versa; a mathematical basis for a result that might have been intuitively obvious.
	en.wikipedia.org /wiki/Mathematical_modelling_in_epidemiology (1293 words)

	Epidemic - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		When each infected individual is infecting more than one other individual, so that the number of infected individuals is growing exponentially, the disease is in an epidemic state.
		Thus even if the number of people affected is small, the phenomenon may still be called an epidemic, although for small epidemics the term "outbreak" is more often used.
		is the basic reproduction number of the infection and S is the proportion of the population who are susceptible to the infection.
	www.lexington-fayette.us /project/wikipedia/index.php/Epidemic (257 words)

	Basic reproduction number
		In epidemiology, the basic reproduction number of an infection is the number of people a single infected individual will infect, in a population with no immunity to the disease.
		This, however, cannot continue indefinitely: eventually the number of susceptible individuals will be depleted.
		They will either have died, or have survived infection and gained immunity to the disease, so limiting the spread of infection.
	www.arikah.com /encyclopedia/Basic_reproduction_number (213 words)

	Science Fair Projects - Endemic (epidemiology)
		In a population with some immune individuals, the basic reproduction number multiplied by the proportion of susceptible individuals in the population (S) must be 1.
		This takes account of the probability of each individual who the disease may be transmitted to actually being susceptible to it, effectively discounting the immune sector of the population.
		In this way, the infection neither dies out nor does the number of infected people increase exponentially but the infection is said to be in an endemic steady state.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Endemic_%28epidemiology%29 (536 words)

	CDC - Ring Vaccination and Smallpox Control
		In Figure 3A and B, the distribution of the total number of infected persons (excluding those who were vaccinated in time to prevent symptomatic infection) and of the time until recovery of the last infected patient is shown for 500 simulation runs with the baseline parameters (Table).
		The average number of infected persons drops to 6 (range 1–43 persons), excluding the identified infected contacts who are vaccinated or monitored and to 14 (range 1–96 persons), including the vaccinated and monitored infected contacts.
		While the number of cases increases almost linearly with the number of index cases, the dependency on the time to diagnosis shows the influence of the variable infectiousness during the infectious period.
	www.cdc.gov /ncidod/EiD/vol10no5/03-0419.htm (4929 words)

	DIMACS Summer School Tutorial on Dynamic Models of Epidemiological Problems
		The basic reproduction number is estimated for many directly transmitted diseases, herd immunity is defined, and the fraction that must be vaccinated to obtain herd immunity is determined for diseases such as measles, rubella, mumps, chickenpox, influenza, polio, and smallpox.
		Values of the basic reproduction number and contact number are estimated for various diseases including measles in Niger, Africa and pertussis in the United States.
		Relationships are given between the basic reproduction numbers for heterogeneously mixing populations and "equivalent" homogeneously mixing populations.
	dimacs.rutgers.edu /Workshops/EpidTutorial/abstracts.html (2099 words)

	Optical disk device for record and reproduction of additional information besides reproduction of basic one - Patent ...
		On a record surface of an optical disk whereon basic information is recorded in a first mode of using surface irregularities, such as pits and lands, a layer of an information recording medium is formed for record and reproduction of additional information in a second mode which is different from the first mode.
		Supplied with the basic information signal from the optical head 17 in the manner which will presently become clear, a basic information reproducing circuit 18 reproduces the basic information as a basic reproduction.
		It is to be noted that such a separating arrangement is connected to the basic information reproducing circuit 18 and to the additional information recording and reproducing circuit 23 and that separation of the basic and the additional information signals results in separation of the basic and the additional reproductions from each other.
	www.freepatentsonline.com /5287335.html (3012 words)

	Emerging Infectious Diseases: Ring vaccination and smallpox control
		The number of contacts on day [tau] of the infectious period in the close contact ring follows a Poisson distribution with mean [[mu].sub.[tau].sup.(1)], and in the casual contact ring this number follows a a negative binomial distribution with mean [[mu].sub.[tau].sup.(2)].
		The basic reproduction number [R.sub.0] describes the average number of secondary cases produced from contact with an infected person during the infectious period and without intervention.
		We use the parameter [a.sub.1] in the function describing the transmission probability (Table) to vary the basic reproduction number, i.e., if we want to simulate an outbreak under the assumption that [R.sub.0] is 5, we chose [a.sub.1] accordingly.
	www.findarticles.com /p/articles/mi_m0GVK/is_5_10/ai_n6090328 (1334 words)

	Workshop on Mathematical Epidemiology: Abstracts
		These expressions are used to estimate the basic reproduction number for measles in Niger, Africa, where the population size is growing rapidly, and for pertussis in the United States, where the population size is nearly constant.
		Taking the cumulative number of transitions from the susceptible state to the infectious state and that from the infectious state to the recovery state as submartingales, we derive the intensity processes for submartingales using binomial distribution (for homogeneous population) and generalized binomial distribution (for heterogeneous population) to form martingale differences.
		Finally, estimates of the basic reproductive rate and vaccine efficacy are used to determine the threshold value for the fraction of susceptible population requiring immunization in order to prevent the spread of an infectious disease from becoming an epidemic.
	www.pims.math.ca /activities/epid.abstracts.html (4389 words)

	The transmission dynamics of influenza A at Hong Kong live bird markets
		Loosely speaking, it is given by the number of secondary infections produced by one infected individual (chicken) in a susceptible population (market).
		As the figure shows, the basic reproduction number increases as the rate of demographic turnover decreases.
		It is due to the fact that the reproduction number in Figure 3 refers to the invasion prospects of a pathogen in a population of susceptible individuals, while Figure 2 refers to the equilibrium prevalence.
	www.cvmbs.colostate.edu /aphi/isvee/vanBoven084.htm (1088 words)

	The estimation of the basic reproduction number for infectious diseases.
		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.
		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.
	www.aegis.com /aidsline/1994/mar/M9430406.html (416 words)

	Nat' Academies Press, Predicting Invasions of Nonindigenous Plants and Plant Pests (2002)
		the average number of offspring or infectious units from a single organism or infectious agent.
		basic reproduction number (Ro): the average number of offspring or infectious units from a single organism or infectious agent.
		carrying capacity: the theoretical maximum number of individuals in a population that can be supported by a defined set of conditions in an environment.
	books.nap.edu /books/0309082641/html/176.html (1832 words)

	No Title
		The use of mathematical modeling as a tool for disease control has historically relied on threshold results, in which a certain factor related to disease transmission must be changed beyond a given level in order to eradicate the disease.
		, which represents the average number of secondary infections caused by one infective in a pool of susceptibles.
		The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one.
	www.uwm.edu /~gb/COLLOQUIA/02-03-01 (261 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The contact number of individuals contacts in unit time tends to saturate, that is, the number of contacts grow less rapidly as population size increases.
		The basic reproduction number which determines the outcome of the disease is identified; if the basic reprodu ction number is not greater than 1, the infected fraction of the population disappears,so the disease dies out, If the basic reproduction number is greater 1, the infected fraction persists, so the disease remains the endemic.
		The results show that the basic reproduction number of the SEIS model with the saturating contact rate is less than that of the SEIS model with the linear or constant contact rate.
	unit.xjtu.edu.cn /unit/xb/zrb/02/0202/xbe2023.html (169 words)

	J Epidemiol Community Health -- eLetters for Data Supplement:
		The drastic decrease in the mean effective reproduction number after April 29 further confirms the fact that the turning point for the outbreak to subside had occurred around April 29 [4].
		It is especially true with the basic reproductive number R0, or its variant the effective reproductive number at time t Rt, which has been estimated for the recent SARS outbreaks in Beijing, Hong Kong,, Toronto, Taiwan, and Singapore in several recent articles (e.g.
		R0, the average number of secondary infections caused by an infective person upon entering a totally susceptible population, is a useful tool to gauge the initial trend of an epidemic.
	jech.bmjjournals.com /cgi/eletters/57/6/DC1 (1843 words)

	Antiviral Drug Use during Influenza Pandemic \| CDC EID
		Resistance to amantadine has been demonstrated in a number of avian H5 strains (11) and its use for treatment of influenza is not recommended (12).
		The model was used to simulate a number of scenarios, on the basis of contingency plans and previous pandemics, to investigate the effect of targeting NIs to different age and risk groups on the expected number of hospitalizations during a pandemic.
		The fit of the model to the data is shown in Figure 4A, from which is derived a 15% residual immunity from the first wave and a 65% serologic attack rate for the second wave, which produces an effective reproduction number of 1.85 for the second wave.
	www.cdc.gov /ncidod/EID/vol11no09/04-1344.htm (4232 words)

	Zeitschrift für Analysis und ihre Anwendungen, Vol. 19, No. 1, pp. 61-75, 2000 (Site not responding. Last check: 2007-11-05)
		Monotonicity of the Number of Passages in Linear Chains and of the Basic Reproduction Number in Epidemic Models
		Abstract: In models for infectious diseases, the basic reproduction number is the crucial parameter which determines the possibility of an outbreak.
		For a class of epidemic models with pair formation models and infectivity depending on time since infection it is shown that the basic reproduction number is a monotone function of infectivity.
	www.mat.ub.es /EMIS/journals/ZAA/1901/5.html (200 words)

	Parasite transmission
		C is the number of secondary cases which arise from the bites taken by all mosquitoes on one infectious person in one day.
		In this case, the most appropriate definition of the basic reproductive rate is the number of infected ticks that would arise after one cycle of transmission if one infected tick were placed in completely susceptible populations of ticks and cattle.
		The value of the basic reproductive rate is 23, and the expected proportion of animals in each infection state is given in Table 1.
	www.fao.org /wairdocs/ilri/x5441e/x5441e06.htm (12275 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		ESTIMATION OF THE BASIC REPRODUCTION RATIO (Ro) FOR SHIGA TOXIN- PRODUCING ESCHERICHIA COLI O157:H7 (STEC O157) IN BEEF CALVES Author(s): LAEGREID, WILLIAM W. Interpretive Summary: Cattle are a major reservoir of Escherichia coli O157:H7, a bacterial serotype that has caused numerous foodborne outbreaks of severe, occasionally fatal, human disease.
		The basic reproduction ratio (Ro) is a term used to describe transmission of infectious agents in populations.
		It is roughly equivalent to the number of animals that become infected through contact with one infectious individual.
	www.marc.usda.gov /marc/InterpretiveSummaries/meat%20safety/AHU-152662.txt (197 words)

	BioMed Central \| Full text \| A double epidemic model for the SARS propagation
		we take away the number of confirmed SARS cases from the Amoy Gardens and those from the local hospitals, then most of the daily new number of confirmed cases from the community stayed around 15 to 25 (of course this level went down after strong confinement directives were implemented by the Hong Kong government).
		The statistics on the numbers of SARS cases in Beijing are obtained from http://www.moh.gov.cn/zhgl/yqfb/index.htm.
		The statistics on the numbers of SARS cases in Inner Mongolia are obtained from http://www.moh.gov.cn/zhgl/yqfb/index.htm.
	www.biomedcentral.com /1471-2334/3/19 (7161 words)

	[No title]
		We derive explicit formulas for the reproductive number and investigate existence of the endemic equilibrium.
		Low active individuals reduce their number of daily contacts due to the news of a smallpox outbreak in the population, whereas highly active individuals continue having a high average number of contacts per day.
		The typical pattern when a new disease invades a population is that an epidemic may occur, with an increase in the number of infectives followed by a decrease to zero.
	cnls.lanl.gov /~ccc/cmeg/abstracts.htm (3338 words)

	CDC - Ring Vaccination and Smallpox Control
		The distribution of A, the total number of infected persons excluding those infected contacts who were vaccinated on time to prevent disease...
		The effective reproduction number is then 0.96; 93.0% of transmissions are in the casual contact ring.
		The mean number of infected persons increases by a factor of 5, and the range of possible outcomes increases such that epidemics with several hundreds of infected persons are possible.
	www.cdc.gov /ncidod/eid/vol10no5/03-0419.htm (4929 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The basic reproductive rate or the intrinsic rate of reproduction is the number of secondary infections caused by a single infectious case.
		If this number is greater than one, on the average, a disease will take off.
		If this number is less than one, on the average, a disease will eventually fade from a population.
	www.askmytutor.co.uk /b/ba/basic_reproductive_rate.html (99 words)

	Quantification of intrinsic residual viral replication in treated HIV-infected patients -- Fraser et al. 98 (26): 15167 ...
		The basic reproduction number is the number of new cells that an infected cell infects before it dies, in the absence of density-dependent
		as the number of secondary infections caused by an infected cell
		The measure used was approximately equal to the number of new mutations generated in the viral population, and thus also to
	www.pnas.org /cgi/content/full/98/26/15167 (3255 words)

	Cynthia Lord Vero Beach (Site not responding. Last check: 2007-11-05)
		Basic and applied research on modeling and quantitative biology of insects of medical and veterinary importance and vector-borne pathogens.
		Implications for seasonality and other complexities on the invasion and persistence of vector borne disease; sensitivity analyses of vector-borne virus epidemiology generating priority list for empirical research (St. Louis encephalitis, West Nile, African horse sickness viruses).
		Vector-borne disease and the basic reproduction number: a case study of African Horse sickness.
	entnemdept.ifas.ufl.edu /lord.htm (270 words)

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