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Auditory-evoked brainstem potentials are helpful to docu- Detection of copper in hepatocytes by routine histochemical ment the degree of functional impairment and the improvement evaluation is highly variable buy 30 mg nifedipine with amex. The Genetic testing amount of copper varies from nodule to nodule in the cirrhotic liver and may vary from cell to cell in pre-cirrhotic stages purchase nifedipine 30mg without a prescription. The Direct molecular-genetic diagnosis is difﬁcult because of more absence of histochemically identiﬁable copper does not exclude than 500 possible mutations; except for a few more frequent Wilson’s disease purchase nifedipine 30mg on line. Furthermore, most patients by various methods, including the rhodanine or orcein stain. Ultrastructural analysis of liver specimens at the time steato- Comprehensive molecular-genetic screening takes several sis is present reveals speciﬁc mitochondrial abnormalities . The most ease, both for conﬁrmation purposes and to facilitate the subse- striking alteration is increased intracristal space with dilatation quent screening of family members. In By contrast, allele-speciﬁc probes allow direct identiﬁcation of the absence of cholestasis, these changes are considered to be a mutation and this can be rapid and clinically very helpful. At later stages ever, thiscanonly beaccomplished ifamutationoccurswitharea- of the disease, dense deposits within lysosomes are present. In those cases, identiﬁcation of a mutation can sup- Neurologic ﬁndings and radiologic imaging of the brain port the diagnosis, while identiﬁcation of two mutations will con- ﬁrm the diagnosis. Consultation to identify the most common mutations, these recommendations with a neurologist should be sought for evaluation of patients may change. Acute liver failure due to Wilson’s disease Neurologic disease may manifest as motor abnormalities with Parkinsonian characteristics of dystonia, hypertonia and rigidity, The most challenging aspect is the diagnosis of acute liver failure choreic or pseudosclerotic, with tremors and dysarthria. Due to due to Wilson’s disease, since mortality without emergency liver the great variability of neurological signs, differences in their transplantation is very high. There is not yet a transferases, provide the most rapid and accurate method for commonly accepted scale which describes neurological signs diagnosis of acute liver failure due to Wilson’s disease . However, these ﬁndings were challenged by phy of the brain may detect structural abnormalities in the basal other authors. Abnormal ﬁndings are not limited to this region, and tional Wilson’s disease diagnostic parameters (ceruloplasmin, other abnormalities have been described. A characteristic ﬁnding serum or urinary copper) are less sensitive and speciﬁc but in Wilson’s disease is the ‘‘face of the giant panda’’ sign [70,71], but important for the diagnosis . Signiﬁcant abnormalities on brain imaging may even be present in some indi- viduals prior to the onset of symptoms . There is a lack of high-quality is justiﬁed given the potential devastating course of Wilson’s dis- evidence to estimate the relative treatment effects of the avail- ease. There is difﬁculty in diagnosing heterozygote carriers with able drugs in Wilson’s disease. Therefore, multicentre prospective certainty, but siblings of an index case with a documented muta- randomized controlled comparative trials are necessary . If the mutation(s) of the index case are not detected, pedigree D-Penicillamine analysis using haplotypes based on polymorphisms surrounding the Wilson’s disease gene is available. This analysis requires the The major effect of D-penicillamine in Wilson’s disease is to identiﬁcation of an index patient with the unquestionable diag- promote the urinary excretion of copper. Dosing in children is 20 mg/kg/day rounded off in the index patient and his/her family. The inheritance of the to the nearest 250 mg and given in two or three divided doses. Since D-penicillamine tends to Genetic testing is the only reliable method to separate heterozy- interfere with pyridoxine action, supplemental pyridoxine gote from homozygote siblings. D-penicillamine interferes with collagen cross-linking  and has some immunosuppres- sant actions [90,91]. Treatment Adequacy of treatment can be monitored by measuring 24- hour urinary copper excretion while on treatment. This is highest A number of drugs are available for the treatment of Wilson’s dis- immediately after starting treatment and may exceed 16 lmol ease, including D-penicillamine, trientine, zinc, tetrathiomolyb- (1000 lg) per 24 h at that time. For long-term treatment, the Recommendation 1 • Wilson’s disease should be considered in any individual • A low serum ceruloplasmin level should be taken with liver abnormalities or neurological movement as evidence for the diagnosis of Wilson’s disease. Lowering the threshold to • Kayser-Fleischer rings should be sought by slit-lamp >0. In untreated treatment in all patients with neurologic Wilson’s disease patients, normal hepatic copper content and should be part of the evaluation of any patient (<0. Serum ceruloplasmin may decrease after effects are rare and include nephrotoxicity, myasthenia gravis initiation of treatment. Urinary copper excretion should run in , polymyositis, loss of taste, immunoglobulin A depression, the vicinity of 3–8 lmol per 24 h on treatment. Hepatic siderosis has been reported in trea- therapeutic efﬁciency, urinary copper excretion after 2 days of ted patients with reduced levels of serum ceruloplasmin and D-penicillamine cessation should be 61. Overtreatment with pen- the estimate of non-ceruloplasmin bound copper shows normal- icillamine may lead to a reversible sideroblastic anemia and ization of non-ceruloplasmin bound copper concentration with hemosiderosis. Trientine (triethylene tetramine dihydrochloride or 2,2,2-tetra- D-penicillamine is rapidly absorbed from the gastrointestinal mine) was introduced in 1969 as an alternative to D-penicilla- tract with a double-peaked curve for intestinal absorption mine. If D-penicillamine is taken with a meal, its absorption chemically distinct from D-penicillamine. Once absorbed, 80% of groups and copper is chelated by forming a stable complex with D-penicillamine circulates bound to plasma proteins. In patients with the administered trientine and about 8% of the biotransformed symptomatic liver disease, recovery of synthetic liver function trientine metabolite, acetyltrien, ultimately appear in the urine. The potency of trientine as copper chelator in compari- to signiﬁcant progression of liver disease and liver failure within son to D-penicillamine is controversial [95,104]. D-penicillamine may mobilize different pools of body copper In patients with neurologic Wilson’s disease, improvement of . Worsening of neurologic symptoms has been reported in three divided doses, with 900–1500 mg/day used for mainte- 10–50% of patients treated with D-penicillamine during the initial nance therapy. In a recent series, neurologic worsening lished, but the dose generally used is 20 mg/kg/day rounded off occurred on all three treatments used for Wilson’s disease (D- to the nearest 250 mg, given in two or three divided doses. Trien- penicillamine, trientine, zinc), but mainly with D-penicillamine, tine should be administered 1 h before or 3 h after meals. Trien- penicillamine may be enhanced by starting with incremental tine tablets may not be stable for prolonged periods at high ambi- doses, 125–250 mg/day increased by 250 mg increments every ent temperature, which is a problem for patients travelling to 4–7 days to a maximum of 1000–1500 mg/day in 2–4 divided dos- warm climates. Administration of doses 1500 mg per day or higher at once Trientine is an effective treatment for Wilson’s disease mayleadtorapidandoftenirreversibleneurological deterioration. Trientine, while being developed for use in patients Rapid re-administration of the treatment in patients who stopped who are intolerant of penicillamine, has also been shown to be it for longer time may also evoke irreversible neurological signs. In general, adverse Severe side effects requiring the drug to be discontinued occur effects due to D-penicillamine resolve when it is substituted for in approximately 30% of patients [95,98]. Early sensitivity reac- trientine and do not recur during prolonged treatment with tions marked by fever and cutaneous eruptions, lymphadenopa- trientine. In these conditions, D-penicillamine of trientine and iron should be avoided because the complex with should be discontinued immediately. A reversible sideroblastic anemia may be a nephrotoxicity, usually heralded by proteinuria or the appear- consequence of overtreatment and resultant copper deﬁciency. However, these patients reactions include a lupus-like syndrome marked by hematuria, were almost all uniformly treated previously with D-penicilla- proteinuria, and positive antinuclear antibody, and with higher mine, so the true frequency of this reaction when trientine is used dosages of D-penicillamine no longer typically used for treating de novo is unknown. Dermatological toxici- Adequacy of treatment is monitored by measuring 24-hour ties reported include progeric changes in the skin and elastosis urinary copper excretion (after 2 days of cessation of therapy) perforans serpingosa , and pemphigous or pemphigoid and by measuring non-ceruloplasmin bound copper. Gastric irritation is a common prob- lem and may be dependent on the salt employed. As yet, clinical experience with this effective than chelating agents in the treatment of established drug is limited. The control of free copper was prospectively stud- Wilson’s disease, although data are limited and uncontrolled ied as initial anti-copper treatment in neurologically presenting . Although zinc is currently reserved for maintenance treat- Wilson’s disease patients . While zinc monotherapy appears to be effec- was associated with signiﬁcant spikes in serum free copper levels. Hepatic deterioration has been occasionally reported include bone marrow depression , hepatotoxicity , and when zinc was commenced and was fatal in one case . Thus, overly aggressive copper removal, which causes neurological dys- exclusive monotherapy with zinc in symptomatic Wilson’s liver function. The outcome of exclusive Zinc zinc therapy was generally good in cases of neurologic disease. A less satisfactory outcome in hepatic disease may relate to less Zinc was ﬁrst used to treat Wilson’s disease by Schouwink in efﬁcient de-coppering.
The development of The Council of Ministers Recommendation generic 20 mg nifedipine, referred European Guidelines for Quality Assurance in Colorectal to earlier in this section nifedipine 30 mg low cost, provides strong guidelines Cancer Screening are expected to be published in for the consideration of gender in health policy proven nifedipine 30 mg. White Paper in 20078 which recognises children as the Ô Health information and knowledge which includes priority group without reference to the need for gen- action on health indicators and ways of dissemi- dered approach to implementation. In a specific call for tender, im- health to agriculture, transport, education and sports. The and invited all Member States to take common action Commission organised a conference in Spring 2009 to to implement national population-based screening explore the impact of gender on mental health. However, most gender- The Portal is also an important source of information based inequities reported affected women and little for health professionals, administrations, policy mak- was said about men. The current health programme, ers and other stakeholders including the general public. Together for Health: Health Programme (2008-2013), Thext and links provided in the men’s health section fall mentioned previously, aims to support the development short of providing a meaningful description of and infor- of strategies and measures on socio-economic health mation about men’s health issues determinants and identifying health inequalities using The Commission has so far funded two consecutive reports data from the Community health information system. The European Men’s Health Forum’s, Report whether inequalities relating to men’s health will be on the State of Men’s Health in 17 European Countries11, included within the scope of the Commission’s review. Through Europe-wide smoking prevention and cessation activi- a collaboration with the European Men’s Health Forum, ties under the current health programme. Indica- reduction of injuries and deaths from alcohol-related road tors are at the crossroads of policy questions and data accidents; preventing harm among adults and reducing sets. They are therefore expected to be broken down the negative impact on the workplace. Female spe- The Commission funds the development of activities cifc interventions (cervical and breast cancer) are the on drug treatment, prevention, treatment and harm re- only ones documented at present. The second Pub- The European Community is actively developing a lic Health Programme (2008-2013) supports actions comprehensive tobacco control policy, which is char- on drug prevention in the strand “Promoting Health”. The forum aims progress health, however men’s health has not been recognised this issue through debate with stakeholder groups, as a particular area for public health concern so far. Long overlooked, men’s However attempts to make an effective use of gender in health now deserves our full attention. It aims to promote collaboration between inter- ested individuals and organisations on the development and application of health policies, research, educa- tion and prevention programmes. Council Recommenda- pendent expert report commissioned by and published under the tion of 2 December 2003 on cancer screening. Council of the auspices of the United Kingdom Presidency of the European Un- European Communities: Brussels; 2003. Brussels: European pean Parliament, the European Economic and Social Commit- Commission of the European Communities; 2007. Treaty of Amsterdam Amending the Treaty on European Union, Member States in reducing alcohol related harm. University of Hamburg Centre for Interdisciplinary Addiction tain Related Acts, 1997 O. Quality of treatment services in Europe – drug Establishing the European Community, Feb. This may seem like a rather fundamental question to ask at the beginning of a review of policy and progress in male health across eleven countries. Of course the health of every individual man everywhere in the world matters to him and to the people who care about him. The evidence about whether men’s health is important to politicians and health planners however, is rather less convincing. Campaigners for better male health from three continents report in this paper that, despite enormous progress in public health and the sophistication of modern treament approaches, men consistently suffer more serious illness than women and die at an earlier age. H igh blood pressure is danger- ous because it makes the heart work too hard and contributes to atherosclerosis (hardening of the arteries). It increases the risk of heart disease (see box 1) and stroke, which are the first- and third-leading causes of death among Americans. H igh blood pressure also can result in other conditions, such as congestive heart failure, kidney disease, and blindness. When you have more than one risk factor for heart disease, your risk of developing heart disease greatly multiplies. Risk factors you can control: Risk factors beyond your control: • High blood pressure • Age (55 or older for men; 65 or older for women) • Abnormal cholesterol • Family history of early heart disease (having a father or •Tobacco use brother diagnosed with heart disease before age 55 or • Diabetes having a mother or sister diagnosed before age 65) • Overweight • Physical inactivity A blood pressure level of 140/90 m m H g or higher is considered high. If your blood pressure is between 120/80 m m H g and 139/89 m m H g, then you have prehypertension. This m eans that you don’t have high blood pressure now but are likely to develop it in the future unless you adopt the healthy lifestyle changes described in this brochure. So high blood pressure is a condition that m ost people will have at som e point in their lives. Both num bers in a blood pressure test are im portant, but for people who are age 50 or older, systolic pressure gives the m ost accurate diagnosis of high blood pressure. Make changes in what you eat and drink, be physically active, and lose extra weight. Hypertension can If you have high blood pressure, you and your health care provider need to work together as almost always be a team to reduce it. Together, you prevented, so these should come up with a plan and timetable for reaching your goal. M onitoring your blood pressure at hom e between visits to your doctor can be helpful. H aving a fam ily m em ber who knows that you have high blood pressure and who under- • Eat foods with stands what you need to do to lower your blood pressure often m akes it easier to m ake less sodium (salt). If you have high blood pressure, following these steps will help you control your blood pressure. This brochure is designed to help you adopt a healthier lifestyle and rem em ber to take prescribed blood pressure-lowering drugs. Following the steps described will help you prevent and control high blood pressure. Losing even 10 pounds can lower your blood pressure— and losing weight has the biggest effect on those who are overweight and already have hypertension. And being overweight or obese increases your chances of developing high blood cholesterol and diabetes— two m ore risk factors for heart disease. It gives an approxim ation of total body fat— and that’s what increases the risk of diseases that are related to being overweight. Another reason is that too m uch body fat in the stom ach area also increases disease risk. A waist m easurem ent of m ore than 35 inches in wom en and m ore than 40 inches in m en is considered high. If you fall in the obese range according to the guidelines in box 4, you are at increased risk for heart disease and need to lose weight. You also should lose weight if you are overweight and have two or m ore heart disease risk factors. This is the healthiest way to lose weight and offers the best chance of long-term success. Just how m any calories you burn daily depends on factors such as your body size and how physically active you are. So, to lose 1 pound a week, you need to eat 500 calories a day less or burn 500 calories a day m ore than you usually do. It’s best to work out som e com bination of both eating less and being m ore physically active. As you lose weight, be sure to follow a healthy eating plan that includes a variety of foods. All you need is 30 m inutes of m oderate-level physical activity on m ost days of the week. Exam ples of such activities are brisk walking, bicycling, raking leaves, and gardening. For instance: Use stairs instead of an elevator, get off a bus one or two stops early, or park your car at the far end of the lot at work. If you already engage in 30 m inutes of m oderate-level physical activity a day, you can get added benefits by doing m ore. Engage in a m oderate-level activity for a longer period each day or engage in a m ore vigorous activity. M ost people don’t need to see a doctor before they start a m oderate-level physical activity.
Gastrointestinal case studies 5 Thomas L (2005) Current management options for irritable bowel syndrome nifedipine 20 mg overnight delivery. Case study level Ma – Duodenal ulcer Learning outcomes Level M case study: You will be able to: I interpret clinical signs and symptoms I evaluate laboratory data I critically appraise treatment options I state goals of therapy I describe a pharmaceutical care plan to include advice to a clinician I describe the prognosis and long-term complications I describe the social pharmacy issues which could include supply (e purchase 30 mg nifedipine visa. Scenario Mr B is a 57-year-old man who was admitted yesterday after starting to pass black stools generic nifedipine 20mg mastercard. He has a two-day history of severe stomach pains and has suffered on and off with indigestion for some months. He was mildly tachycardic (87 bpm) and had a slightly low blood pressure of 115/77 mmHg and was given 1. He has just returned from endoscopy this morning and has been newly diagnosed as having a bleeding duodenal ulcer. He has been written up for his usual medication for tomorrow if he is eating and drinking again. British Society of Gastroenterology Endoscopy Committee (2002) Non-variceal upper gastrointestinal haemorrhage: guidelines. Case study level Mb – Ulcerative colitis Learning outcomes Level M case study: You will be able to: I interpret clinical signs and symptoms I evaluate laboratory data I critically appraise treatment options I state goals of therapy I describe a pharmaceutical care plan to include advice to a clinician I describe the prognosis and long-term complications I describe the social pharmacy issues which could include supply (e. Gastrointestinal case studies 7 Scenario Mrs D has recently been admitted with an episode of acute severe ulcerative colitis. She is currently taking mesalazine 800 mg three times daily and prednisolone 20 mg daily. Her biochemistry results are reported as: Na+ 143 mmol/L (range 133 to 145 mmol/L) K+ 3. Several days later you see Mrs D, who is distressed as she is not responding to treatment and she desperately wants to avoid surgery. The consultant has sug- gested that ciclosporin may be an option, and she asks to talk to you about it. Mpofu C and Ireland A (2006) Inﬂammatory bowel disease – the disease and its diagno- sis. St Clair Jones A (2006) Inﬂammatory bowel disease – drug treatment and its implications. Answers Case study level 1 – ulcerative colitis – see page 1 1a What is ulcerative colitis? Ulcerative colitis is an inﬂammatory disease of the lower gastrointestinal tract, which results in episodes of diarrhoea. There may also be extraintestinal symp- toms, including anaemia, arthritis, dermatological problems and eye disorders. The exact causes are unclear, although there are several theories, which include genetic, environmental and microbial factors, possibly associated with an inap- propriate immune response. Although anyone can develop ulcerative colitis it appears to be most common in developed countries, and the risk appears greater if a ﬁrst-degree relative has the disease. Patients most commonly present at 20–40 years of age and some studies suggest that ulcerative colitis is slightly more common in women than men. Gastrointestinal case studies 9 3a What is the active ingredient of Predsol and what class of drugs does it come from? Corticosteroids have anti-inﬂammatory and immunosuppressive effects, which reduce the causes of the diarrhoea and thereby settle the disease. Corticosteroids can also cause increased appetite, weight gain, insomnia, depression, osteoporosis, peptic ulceration and glucose intolerance, leading to diabetes. Immunosupression caused by this type of treatment can lead to an increased susceptibility to infection. Therefore patients taking corticosteroids (usually in high doses) should not be given live vaccines. Although systemic absorption of the prednisolone from the enema probably does occur, especially when the colon is particularly inﬂamed, corticosteroids usually have less systemic effects when given this way. Furthermore, by giving an enema, the drug is being delivered directly to its site of action – remember that in ulcerative colitis the disease is conﬁned to the lower gastrointestinal tract. She could self-administer: I tablets (either plain or enteric coated) I suppositories I foam enemas. This is because they will enter the bloodstream in greater amounts by the oral route and have systemic effects. It is usually recommended that corticosteroids are used in the lowest possible dose for the shortest possible period of time. The suppositories are also easier to use, but, because they only have a local action they are only suitable for localised disease (proctitis). I She should lie on her left side to facilitate the spread of the enema, with either her right leg, or both legs drawn up. I The tip of the enema should be lubricated, with either K-Y jelly or petroleum jelly. I She should gently insert the enema to about half the length of the tip using a gently twisting action. I She should gently and slowly (over 1–2 minutes) roll up the bag so as not to give the enema too quickly. Constipation cannot solely be deﬁned by bowel frequency, as this naturally varies in the population. Simply, constipation is deﬁned as a decrease in the patient’s normal pattern of defecation, although for research purposes other cri- teria are often considered (e. The incidence of constipation is hard to deﬁne, with rates in women stated to be 8. Although his age in itself does not cause constipation, factors such as decreased mobility and decreased dietary intake increase the prevalence of constipation in this group. I Mr A has been taking dihydrocodeine (as part of co-dydramol), one of the adverse effects of which is constipation. Blood in the stools, severe abdominal pain, unintentional weight loss, co-existing diarrhoea, persistent symptoms, tenesemus or failure of previous Gastrointestinal case studies 11 medication. These symptoms can point to more severe disorders such as impaction, or malignancy. From the description of the adverse effects, a stimulating laxative seems most likely, as they commonly cause abdominal cramps. Senna is a stimulant laxative and is available as brown tablets, and so this seems the most likely laxative. Although stimulant laxatives are often considered to be second line, it has been said that laxative choice is best based on symptoms, patients’ preference, adverse effects and cost. In the case of Mr A the stimulant laxatives have the advantage of being fairly quick acting, and are often useful to counteract the effects of decreased bowel motility caused by opioid analgesics. Other types of laxative include the following: I Bulk-forming laxatives (such as ispaghula husk), which work by increasing faecal mass, but they may take several days to become fully effective. They are of most use in those patients that pass small stools and have a diet lacking in ﬁbre (but they should not replace dietary lifestyle measures) I Faecal softeners (such as docusate, which is stimulating but which also has softening properties). They may take several days to become fully effective and it is essential that ﬂuid intake is maintained during their use. I Lifestyle measures may include increased dietary ﬁbre, ensuring an adequate ﬂuid intake, keeping as mobile as possible, etc. I A laxative would seem appropriate at this stage as Mr A is elderly and it is likely that his constipation is drug-induced. I Discuss the adverse effects his wife has experienced and explain that senna is in fact a herbal medicine and that herbal remedies may not necessarily be gentle. If he accepts this suggestion counsel him to take the tablets before bed (as they take 8–10 hours to work). If he is reluctant to try senna explain to him that lactulose is often insufﬁcient alone in treating opioid-induced constipation, and may take 48 hours to work. Bisacodyl may be an alternative stimulant laxative, but is likely to have similar adverse effects. Ensure that the laxative has been taken in an adequate dose for a sufﬁcient amount of time. Ensure that Mr A has been taking a reasonable dose for a reasonable period of time (several days would be needed to assess the efﬁcacy of lactulose).
University of Minnesota Extension Office - "Prevention and Control of Bed Bugs in Residences buy cheap nifedipine 20 mg online," "Traveler Q & A: Preventing Bed Bugs from Hitchhiking to Your Home buy cheap nifedipine 20mg online," and "Control of Bed Bugs in Residences 30 mg nifedipine overnight delivery, Information for Pest Control Companies" (all prepared by Dr. Many models for the spread of infectious diseases in populations have been analyzed math- ematically and applied to speciﬁc diseases. Values of R0 and σ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed. The eﬀectiveness of improved sanitation, antibiotics, and vac- cination programs created a conﬁdence in the 1960s that infectious diseases would soon be eliminated. Consequently, chronic diseases such as cardiovascular disease and cancer received more attention in the United States and industrialized countries. But infectious diseases have continued to be the major causes of suﬀering and mortality in developing countries. Moreover, infectious disease agents adapt and evolve, so that new infectious diseases have emerged and some existing diseases have reemerged . Newly identiﬁed diseases include Lyme disease (1975), Legionnaire’s disease (1976), toxic-shock syndrome (1978), hepatitis C (1989), hepatitis E (1990), and hantavirus (1993). Antibiotic-resistant strains of tuberculosis, pneumonia, and gonorrhea have evolved. Malaria, dengue, and yellow fever have reemerged and are spreading into new regions as climate changes occur. Diseases such as plague, cholera, and hemorrhagic fevers (Bolivian, Ebola, Lassa, Marburg, etc. Surprisingly, new infectious agents called prions have recently joined the previously known agents: viruses, bac- teria, protozoa, and helminths (worms). There is strong evidence that prions are the cause of spongiform encephalopathies, e. Recent popular books have given us exciting accounts of the emergence and de- tection of new diseases [82, 168, 170, 183]. It is clear that human or animal invasions ∗Received by the editors March 6, 2000; accepted for publication (in revised form) May 7, 2000; published electronically October 30, 2000. The emerging and reemerging diseases have led to a revived interest in infec- tious diseases. Mathematical models have become important tools in analyzing the spread and control of infectious diseases. The model formulation process clariﬁes as- sumptions, variables, and parameters; moreover, models provide conceptual results such as thresholds, basic reproduction numbers, contact numbers, and replacement numbers. Mathematical models and computer simulations are useful experimental tools for building and testing theories, assessing quantitative conjectures, answer- ing speciﬁc questions, determining sensitivities to changes in parameter values, and estimating key parameters from data. Understanding the transmission characteris- tics of infectious diseases in communities, regions, and countries can lead to better approaches to decreasing the transmission of these diseases. Mathematical models are used in comparing, planning, implementing, evaluating, and optimizing various detection, prevention, therapy, and control programs. Epidemiology modeling can contribute to the design and analysis of epidemiological surveys, suggest crucial data that should be collected, identify trends, make general forecasts, and estimate the uncertainty in forecasts [100, 111]. Although a model for smallpox was formulated and solved by Daniel Bernoulli in 1760 in order to evaluate the eﬀectiveness of variolation of healthy people with the smallpox virus , deterministic epidemiology modeling seems to have started in the 20th century. In 1906 Hamer formulated and analyzed a discrete time model in his attempt to understand the recurrence of measles epidemics . His model may have been the ﬁrst to assume that the incidence (number of new cases per unit time) depends on the product of the densities of the susceptibles and infectives. Ross was interested in the incidence and control of malaria, so he developed diﬀerential equation models for malaria as a host-vector disease in 1911 . Other determin- istic epidemiology models were then developed in papers by Ross, Ross and Hudson, Martini, and Lotka [18, 60, 66]. Starting in 1926 Kermack and McKendrick published papers on epidemic models and obtained the epidemic threshold result that the den- sity of susceptibles must exceed a critical value in order for an epidemic outbreak to occur [18, 136, 157]. Mathematical epidemiology seems to have grown exponentially starting in the middle of the 20th century (the ﬁrst edition in 1957 of Bailey’s book  is an important landmark), so that a tremendous variety of models have now been formulated, mathematically analyzed, and applied to infectious diseases. Re- views of the literature [21, 39, 60, 65, 67, 102, 107, 109, 199] show the rapid growth of epidemiology modeling. The recent models have involved aspects such as passive immunity, gradual loss of vaccine and disease-acquired immunity, stages of infection, vertical transmission, disease vectors, macroparasitic loads, age structure, social and sexual mixing groups, spatial spread, vaccination, quarantine, and chemotherapy. The breadth of the subject is shown in the books on epidemiology modeling [5, 9, 12, 18, 19, 20, 22, 33, 38, 39, 55, 56, 59, 80, 81, 90, 111, 113, 127, 137, 141, 151, 164, 167, 173, 181, 194, 196]. Compartments with labels such as M, S, E, I, and R are often used for the epidemiological classes as shown in Figure 1. After the maternal antibodies disappear from the body, the in- fant moves to the susceptible class S. Infants who do not have any passive immunity, because their mothers were never infected, also enter the class S of susceptible indi- viduals; that is, those who can become infected. When there is an adequate contact of a susceptible with an infective so that transmission occurs, then the susceptible enters the exposed class E of those in the latent period, who are infected but not yet infectious. After the latent period ends, the individual enters the class I of infectives, who are infectious in the sense that they are capable of transmitting the infection. When the infectious period ends, the individual enters the recovered class R consisting of those with permanent infection-acquired immunity. The choice of which compartments to include in a model depends on the charac- teristics of the particular disease being modeled and the purpose of the model. The passively immune class M and the latent period class E are often omitted, because they are not crucial for the susceptible-infective interaction. The threshold for many epidemiology models is the basic reproduction number R0, which is deﬁned as the average number of secondary infections produced when one infected individual is introduced into a host population where everyone is suscep- tible . For many deterministic epidemiology models, an infection can get started in a fully susceptible population if and only if R0 > 1. Thus the basic reproduc- tion number R0 is often considered as the threshold quantity that determines when an infection can invade and persist in a new host population. Section 2 introduces epidemiology modeling by formulating and analyzing two classic deterministic mod- els. Then thresholds are estimated from data on several diseases and the implications of the estimates are considered for diseases such as smallpox, polio, measles, rubella, chickenpox, and inﬂuenza. This model demonstrates how exponential population growth aﬀects the basic reproduction number R0. These epidemiologic models are based on the demographic models in section 4 with either continuous age or age groups. The two demographic models demonstrate the role of the population reproduction numbers in determining when the population grows asymptotically exponentially. New general expressions for the basic reproduction number R0 and the average age of infection A are obtained. The theoretical expressions in section 6 are used in section 7 to obtain estimates of the basic reproduction number R0 and the average age of infection A for measles in Niger, Africa. In section 8 estimates of the basic reproduction number R0 and the contact number σ (deﬁned in section 2. Because pertussis infectives with lower infectivity occur in previously infected people, the contact number σ at the endemic steady state is less than the basic reproduction number R0. Section 9 describes results on the basic reproduction number R0 for previous epidemiology models with a variety of structures, and section 10 contains a general discussion. Epidemic models are used to describe rapid outbreaks that occur in less than one year, while endemic models are used for studying diseases over longer periods, during which there is a renewal of susceptibles by births or recovery from temporary immunity. The horizontal incidence shown in Fig- ure 1 is the infection rate of susceptible individuals through their contacts with infec- tives. If S(t) is the number of susceptibles at time t, I(t) is the number of infectives, and N is the total population size, then s(t)=S(t)/N and i(t)=I(t)/N are the susceptible and infectious fractions, respectively. This form of the horizontal incidence is called the standard incidence, because it is formulated from the basic principles above [96, 102]. The parameter η has no direct epidemiological interpretation, but comparing it with the standard formulation shows that β = ηN, so that this form implicitly assumes that the contact rate β increases linearly with the population size. Naively, it might seem plausible that the population density and hence the contact rate would increase with population size, but the daily contact patterns of people are often similar in large and small communities, cities, and regions. This strongly suggests that the standard incidence corresponding to v = 0 is more realistic for human diseases than the simple mass action incidence corresponding to v =1.
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