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Observe that the threshold result here involves the initial replacement number so and does not involve the basic reproduction number R0 buy generic suhagra online erectile dysfunction treatment in singapore. Here the contact number remains equal to the basic reproduction number R0 for all time buy suhagra 100 mg without a prescription erectile dysfunction leakage, because no new classes of susceptibles or infectives occur after the invasion buy generic suhagra 100 mg erectile dysfunction consult doctor. For this model the threshold quantity is given by R0 = = /( + ), which is the contact rate times the average death-adjusted infectious period 1/( + ). If 1 or io =0, then solution paths starting in T approach the disease-free equilibrium given by s =1and i =0. If>1, then all solution paths with io > 0 approach the endemic equilibrium given by se =1/ and ie = ( 1)/. If R0 = 1, then the replacement number s is less than 1 when io > 0, so that the infec- tives decrease to zero. However, after the infective fraction has decreased to a low level, the slow processes of the deaths of recovered people and the births of new susceptibles grad- ually (over about 10 or 20 years) increase the susceptible fraction until s(t) is large enough that another smaller epidemic occurs. This process of alternating rapid epi- demics and slow regeneration of susceptibles continues as the paths approach the en- demic equilibrium given in the theorem. At this endemic equilibrium the replacement number se is 1, which is plausible since if the replacement number were greater than or less than 1, the infective fraction i(t) would be increasing or decreasing, respectively. Notice that the ie coordinate of the endemic equilibrium is negative for <1, coincides with the disease-free equilibrium value of zero at = 1, and becomes positive for >1. This equilibrium given by se =1/ and ie = ( 1)/ is unstable for <1 and is locally asymptotically stable for >1, while the disease-free equilibrium given by s = 1 and i =0is locally stable for <1 and unstable for >1. Thus these two equilibria exchange stabilities as the endemic equilibrium moves through the disease-free equilibrium when = 1 and becomes a distinct, epidemiologically feasible, locally asymptotically stable equilibrium when >1. The following interpretation of the results in the theorem and paragraph above is one reason why the basic reproduction number R0 has become widely used in the epidemiology literature. If the basic reproduction number R0 (which is always equal to the contact number when the entire population is susceptible) is less than 1, then the disease-free equilibrium is locally asymptotically stable and the disease cannot invade the population. But if R0 > 1, then the disease-free equilibrium is unstable with a repulsive direction into the positive si quadrant, so the disease can invade in the sense that any path starting with a small positive io moves into the positive si quadrant where the disease persists. The latter condition is used to obtain expressions for R0 in age-structured models in sections 5 and 6. This unrealistically short average lifetime has been chosen so that the endemic equilibrium is clearly above the horizontal axis and the spiraling into the endemic equilibrium can be seen. They unrealistically assume that the population is uniform and homoge- neously mixing, whereas it is known that mixing depends on many factors including age (children usually have more adequate contacts per day than adults). Moreover, dierent geographic and social-economic groups have dierent contact rates. By using data on the susceptible fractions so and s at the beginning and end of epidemics, this formula can be used to estimate contact numbers for specic diseases [100]. Using blood samples from freshmen at Yale University [75], the fractions susceptible to rubella at the beginning and end of the freshman year were found to be 0. For the 1957 Asian Flu (H2N2 type A strain of inuenza) in Melbourne, Australia, the fractions so = 1 and s =0. This approach is somewhat naive, because the average seropositivity in a population decreases to zero as the initial passive immunity declines and then increases as people age and are exposed to infectives. The incidence rate at the endemic equilibrium is iese, so that ie is the incidence rate constant, which with exponential waiting time implies that the average age of infection (the mean waiting time in S) is A =1/ie =1/[ ( 1)]. Data on average ages of infection and average lifetimes in developed countries have been used to estimate basic reproduction numbers R0 for some viral diseases. Because disease-acquired immunity is only temporary for bacterial diseases such as pertussis (whooping cough) and diphtheria, the formula R0 = =1+L/A cannot be used to estimate R0 for these diseases (see section 8 for estimates of R0 and for pertussis). Herd immunity occurs for a disease if enough people have disease-acquired or vaccination-acquired immunity, so that the introduction of one infective into the pop- ulation does not cause an invasion of the disease. Intuitively, if the contact number is, so that the typical infective has adequate contacts with people during the infectious period, then the replacement number s must be less than 1 so that the disease does not spread. This means that s must be less than 1/, so the immune fraction r must satisfy r>1 1/ =1 1/R0. Using the estimates above for R0, the minimum immune fractions for herd im- munity are 0. Although these values give only crude, ballpark estimates for the vaccination-acquired immunity level in a community required for herd immunity, they are useful for comparing diseases. For example, these numbers suggest that it should be easier to achieve herd immunity for poliomyelitis and smallpox than for measles, mumps, and rubella. This conclusion is justied by the actual eectiveness of vaccina- tion programs in reducing, locally eliminating, and eradicating these diseases (eradi- cation means elimination throughout the world). The information in the next section veries that smallpox has been eradicated worldwide and polio should be eradicated worldwide within a few years, while the diseases of rubella and measles still persist at low levels in the United States and at higher levels in many other countries. For centuries the process of variolation with material from smallpox pustules was used in Africa, China, and India before arriving in Europe and the Americas in the 18th century. Edward Jenner, an English country doctor, observed over 25 years that milkmaids who had been infected with cowpox did not get smallpox. In 1796 he started vaccinating people with cowpox to protect them against smallpox [168]. Two years later, the ndings of the rst vaccine trials were published, and by the early 1800s, the smallpox vaccine was widely available. Smallpox vaccination was used in many countries in the 19th century, but smallpox remained endemic. Smallpox was slowly eliminated from many countries, with the last case in the Americas in 1971. The last case worldwide was in Somalia in 1977, so smallpox has been eradicated throughout the world [23, 77, 168]. Most cases of poliomyelitis are asymptomatic, but a small fraction of cases result in paralysis. In the 1950s in the United States, there were about 60,000 paralytic polio cases per year. In 1955 Jonas Salk developed an injectable polio vaccine from an inactivated polio virus. This vaccine provides protection for the person, but the person can still harbor live viruses in their intestines and can pass them to others. In 1961 Albert Sabin developed an oral polio vaccine from weakened strains of the polio virus. This vaccine provokes a powerful immune response, so the person cannot harbor the wild-type polio viruses, but a very small fraction (about one in 2 million) of those receiving the oral vaccine develop paralytic polio [23, 168]. The Salk vaccine interrupted polio transmission and the Sabin vaccine eliminated polio epidemics in the United States, so there have been no indigenous cases of naturally occurring polio since 1979. In order to eliminate the few cases of vaccine-related paralytic polio each year, the United States now recommends the Salk injectable vaccine for the rst four polio vaccinations, even though it is more expensive [50].

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Because many nursing home patients suffer from chronic debilitating conditions order suhagra visa impotence jelly, their assumed cause of death often is unquestioned by physicians purchase discount suhagra erectile dysfunction vacuum device. In fact suhagra 100 mg discount erectile dysfunction joke, researchers have found that heart disease may be over-represented in the general population as a cause of death on death certificates by 8-24%. In the elderly, the overreporting of heart disease as a cause of death is as much as twofold. The study found only 8% of the patients were well nourished, while 29% were malnourished and 63% were at risk of malnutrition. As a result, 25% of the malnourished patients required readmission to an acute-care hospital, compared to 11% of the well- nourished patients. The authors concluded that malnutrition reached epidemic proportions in patients admitted to this subacute-care facility. Studies show that compared to no restraints, the use of restraints carries a higher mortality rate and economic burden. Several studies reveal that nearly half of the listed causes of death on death certificates for elderly people with chronic or multi-system disease are inaccurate. Medco oversees drug-benefit plans for more than 60 million Americans, including 6. Reuters interviewed Kasey Thompson, director of the Center on Patient Safety at the American Society of Health System Pharmacists, who noted: There are serious and systemic problems with poor continuity of care in the United States. The average intake of medications was five per resident; the authors noted that many of these drugs were given without a documented diagnosis justifying their use. Seniors are given the choice of either high-cost patented drugs or low-cost generic drugs. Drug companies attempt to keep the most expensive drugs on the shelves and suppress access to generic drugs, despite facing stiff fines of hundreds of millions of dollars levied by the federal government. One study evaluated pain management in a group of 13,625 cancer patients, aged 65 and over, living in nursing homes. The authors concluded that older patients and minority patients were more likely to have their pain untreated. Carcinogenic drugs (hormone replacement therapy,* immunosuppressive and prescription drugs). Health care is based on the free market system with no fixed budget or limitations on expansion. The federal government does no central planning, though it is the major purchaser of health care for older people and some poor people. Americans are less satisfied with their health care system than people in other developed countries. Huge public and private investments in medical research and pharmaceutical development drive this technological arms race. Any efforts to restrain technological developments in health care are opposed by policymakers concerned about negative impacts on medical-technology industries. The high cost of defensive medicine, with an escalation in services solely to avoid malpractice litigation. The availability and use of new medical technologies have contributed the most to increased health care spending, argue many analysts. The reasons government attempts to control health care costs have failed include: 1. In addition to R&D, the medical industry spent 24% of total sales on promoting their products and 15% of total sales on development. If health care spending is perceived as a problem, a highly profitable drug industry exacerbates the problem. Many argue that reductions in the pre-approval testing of drugs open the possibility of significant undiscovered toxicities. Assessing risks and costs, as well as benefits, has been central to the exercise of good medical judgment for decades. Examples of Lack of Proper Management of HealthCare Treatments for Coronary Artery Disease 1. Both procedures increase in number every year as the patient population grows older and sicker. Rates of use are higher in white patients and private insurance patients, and vary greatly by geographic region, suggesting that use of these procedures is based on non-clinical factors. They reviewed 1,300 procedures and found 2% were inappropriate, 90% were appropriate, and 7% were uncertain. The New York numbers are in question because New York State limits the number of surgery centers, and the per-capita supply of cardiac surgeons in New York is about one-half of the national average. A definitive review published in 1994 found less than 30 studies of 5,000 that were prospective comparisons of diagnostic accuracy or therapeutic choice. Clinical evaluation, appropriate patient selection, and matching supply to legitimate demand might be viewed as secondary forces. Laparoscopic cholecystectomy was introduced at a professional surgical society meeting in late 1989. There was an associated increase of 30% in the number of cholecystectomies performed. Because of the increased volume of gall bladder operations, their total cost increased 11. The mortality rate for gall bladder surgeries did not decline as a result of the lower risk because so many more were performed. When studies were finally done on completed cases, the results showed that laparoscopic cholecystectomy was associated with reduced inpatient duration, decreased pain, and a shorter period of restricted activity. But rates of bile duct and major vessel injury increased and it was suggested that these rates were worse for people with acute cholecystitis. Patient demand, fueled by substantial media attention, was a major force in promoting rapid adoption of these procedures. The major manufacturer of laparoscopic equipment produced the video that introduced the procedure in 1989. Doctors were given two-day training seminars before performing the surgery on patients. In 1992, the Canadian National Breast Cancer Study of 50,000 women showed that mammography had no effect on mortality for women aged 40-50. Incidence of adverse drug reactions in hospitalized patients: a meta-analysis of prospective studies. Patient, provider and hospital characteristics associated with inappropriate hospitalization. The cost of inappropriate admissions: a study of health benefits and resource utilization in a department of internal medicine. Fourth Decennial International Conference on Nosocomial and Healthcare-Associated Infections. Malnutrition and dehydration in nursing homes: key issues in prevention and treatment. Nationwide poll on patient safety: 100 million Americans see medical mistakes directly touching them [press release].

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The technique is excellent for observ- ing hidden objects on people or the cargo in contain- ers objects that is not possible to observe with the usual metal detectors cheap suhagra online mastercard impotence low testosterone. purchase 100 mg suhagra fast delivery erectile dysfunction drug therapy. The most common radioisotope used in diagnosis is technetium-99 suhagra 100mg overnight delivery why alcohol causes erectile dysfunction, but a large number of other isotopes are in use. Diagnosis For diagnostic purposes we use radioactive tracers which emit gamma rays from within the body. The isotopes are generally short-lived and linked to chemical compounds which permit specifc physi- ological processes to be studied. For a number of years the g-radiation was observed using a so-called gamma camera. When this nuclide decays, it emits a positron, which promptly combines with a nearby electron resulting in the simultaneous emission of two g-photons in opposite directions. With the isotope F-18 as the tracer, it has proven to be the most accurate noninvasive method of detecting and evaluating most cancers. The reason for this is that F-18 can be added to glucose and the tumors have an increased rate of glucose metabolism compared to benign cells. Isotopes for diagnosis Let us point out a couple of important requirements for the use of ra- dioisotopes: 1. Due to the requirement of a short half-life mainly or solely artifcially made isotopes comes into question. This implies that the nuclear medicine started when equipment like the cyclotron and neutron sources like the reactor become available in the 1930s and 1940s. Georg de Hevesy and coworkers used Pb-210 (one of the isotopes in the Uranium-radium-series) and studied the absorption and elimination of lead, bismuth and thallium salts by animal organisms. Chieivitz and Georg de Hevesy administered phosphate la- beled with P 32 to rats and demonstrated the renewal of the mineral constituents of bone. George de Hevesy was awarded the Nobel prize in chemis- try for his pioneering work with radioactive tracers. George de Hevesy (1885 1966) 1930s in Berkeley He was awarded the Nobel prize in chemistry for 1943. The University of California in Berkeley has played a sig- for his work on the use of isotopes nifcant role in the start and growth of nuclear medicine. The Lawrence brothers are of Norwegian heritage and Sea- borg is coming from Sweden. Lawrence, the brother of Ernest, made the frst clinical therapeutic application of an artif- cial radionuclide when he used phosphorus-32 to treat leukemia. Also Joseph Gilbert Hamilton and Robert Spencer Stone administered sodium-24 to a leukemia patient. Furthermore, this year Emilio Segre and Seaborg discovered Tc-99m the metastable (excited) Tc-99 isotope. The metastable isotope has a half-life of 6 hours and emit a g-photon with energy 140 keV. Tc 99m is an important isotope and is used in approximately 85 percent Emilio Segr of diagnostic imaging procedures in nuclear medicine. The development of nuclear accelerators in particular the cyclotron made it possible to enter the feld of nuclear medicine. Two scientists are of utmost importance for the construction of the frst accelerators; Rolf Widere and Ernest Lawrence. The development of the cyclotron and the beginning of nuclear medicine is closely connect- ed to California and the Berkeley University. It all started when the oldest of the Lawrence brothers (Ernest) came to Berkeley in 1929. In a linear accelerator charged particles are accelerated in tubes forming a straight line. Lawrence arranged this by letting the particles go in larger and larger circles within a box kept in place by a magnetic feld. Ernest Lawrence Rolf Widere (1901 1958) (1902 1996) Ernest Lawrence is of Norwegian heritage Rolf Widere is Norwegian, born in Oslo. He was He was engaged in the construction of an the father of the frst cyclotrons constructed accelerator, and published these ideas al- in Berkeley. His name is The Radiation Laboratory in Berkeley are connected to important acellerators for radi- named after him. He was an exciting public science center with excit- behind the frst high energy radiation source ing hands-on experiences for learners of all in Norway the betatron from 1953 at The ages. The above picture is a model of a cyclotron placed near the entrance of Lawrence Hall of Science in Berkeley. The Berkeley University developed a number of accelerators and become the place where new isotopes were produced. The leading scientist in the production of new isotopes and elements was Glenn Seaborg. Glenn Seaborg (1912 1999) Glenn Seaborg was a Swedish American (his mother was from Sweden). He also developed more than 100 atomic isotopes, like I-131 and Tc- 99m which are important isotopes for medicine. Seaborg was avarded the Nobel prize for Chem- istry in 1951 together with another Berkeley sci- entist Edwin McMillan. He used for the frst time a radioactive isotope in the treatment of a human disease (leukemia). John Lawrence became known as the father of nuclear medicine and Donner laboratory is considered the birthplace of this feld. Hal Anger (also a Donner man) invented in John Lawrence Hal Anger 1958 the gamma-camera also called Anger (1904 1991) (1920 2005) camera. This is also called Anger camera and consisted of a large fat scintilla- tion crystal and a number of photomultipliers. They used I-131 labeled insulin to measure the reaction between an antigen and antibody. David Kuhl 193 Some of the isotopes used in nuclear medicine The use of radioactive isotopes in research and medicine can be divided in three groups. Isotopes used as tracers A radioactive isotope attached to an important molecule can tell where it is. Isotopes emitting g-rays are easily observed, but also pure b-emitters like H 3 (tritium) and C 14 can be used. Thus, Melvin Calvin used C 14 to the exploration of photosynthetic carbon dioxide reduction. The Hershey Chase experiment A very well known experiment with radioactive tracers was the Hershey Chase experiment from 1952. Alfred Hershey and Martha Chase used the isotopes P 32 (b-emitter with half-life 14 days) and S 35 (b-emitter with half-life 87 days). Alfred Hershey (1908 1997) was the principal investiga- Numerous experiments within bio- tor, whereas Martha Chase (1927 2003) was the lab.