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By G. Sibur-Narad. Southwest Baptist University. 2018.

These stresses can interpersonal relationships during training and throughout spill over into personal life buy cheap isoptin 120mg on-line hypertension complications, straining relationships and leading one s career generic isoptin 40 mg overnight delivery blood pressure range. Specifc attention will be paid to physicians rela- to family discord and isolation from friends generic 120mg isoptin with mastercard blood pressure medication and juice. They identifed four risk factors for a disrupted quences of work-home interference among medical residents. In addition, describe some interventions that can improve the personal many doctors are embarrassed to fnd that they need relation- relationships of physicians. They are often wounded healers who have already faced stressors that make them vulnerable to mental illness, Case or who have undiagnosed mental health problems (e. Most of the residents in the such problems are likely to be compounded in spousal rela- program have intimate partners, and several have children. Although the One of the residents told the program director that this onset of relationship diffculties can be insidious, physicians resident had not had a chance to spend meaningful time should be alert to the warning signs, such as more frequent with their partner, with the exception of a yearly vacation. Useful strategies that develop and safeguard intimacy in a relationship include: protecting time to communicate with one s partner; reading Introduction about the dynamics of relationships; attending a marital retreat; Certain traits that seem to go with the territory of medicine attending couples therapy; and taking time to manage one s can have a detrimental effect on physicians personal lives. Refection for educators Warde and colleagues, reported increased marital and parental Get to know the spouses and signifcant others in the lives satisfaction have been closely associated with a decrease in of the residents in your program early on in residency confict between professional and familial roles. Educate residents spouses about the physician the confict between the demands training and home-life, and health resources available to their families (e. These individuals are often the frst to in both parental and marital satisfaction. Adequate vacation time, fexible Case resolution work hours and equitable part-time work are conditions of The program director organizes a day-long retreat for the employment that are conducive not only to improved family residents and their signifcant others. The program director life and mental well-being but also to greater job satisfaction brings in a well-known speaker to discuss issues surround- and productivity. Physicians are most satisfed as parents when ing physician health, including work-lifebalance, ways to they have a supportive spouse and when the work home con- maintain healthy intimate relationships, and recognizing ficts of both partners are minimal. The resident body fnds the expe- medical practice can also affect physicians relationships with rience very useful and decide to make this an annual event their children. For instance, Armstrong s group, found that to help prevent family stress related to residency training physicians who worked for a salary were more fulflled in their and to help recognize the roles that each of their families parental role than physicians who worked on fee-for-service play in their own residency program. Finally, the employment status of one s spouse seems to play a role in parental satisfaction. It is also im- medical families, and portant to value the work and other pursuits of one s partner, explore challenges specifc to those relationships. Case As seductive as the practise of medicine can be, Michael Myers A resident requests a meeting with their supervisor over reminds us to say yes to the relationship and practise say- coffee. The resident becomes distraught while disclosing ing no to other offers (Myers 2001). Spend a minimum of that she miscarried her frst pregnancy three weeks ago twenty minutes alone with your spouse each day and plan a and that her partner, a more senior resident, is preoccu- date together every week. The resident acknowledges that her partner has tried Monica Hill and Nancy Love quote the novelist Henry James to be supportive, but feels that he just doesn t get it. For physicians as for anyone else, this means having population, domestic violence and abuse occurs in medical time together to develop the essential advantage of such rela- families too. Confict between work and familial roles is inevitable at times, whether one or both partners are physicians. Classically, role Work and family life strain has been more frequently noted among female physi- The issue of deferring intimacy in favour of medical work has cians, but in reality male physicians experience it as well. Half been described in the literature on medical marriages (Myers of married women physicians are married to other physicians 2001 and Gabbard 1989). Dual-physician relationships bring sional advancement over the nurturing of intimate relation- certain challenges, such as complicated schedules and career ships, working long hours at the expense of their home lives. Careers postpone their investment in the emotional bank account of can be shaped, reshaped and salvaged more easily than rela- their families or in some cases, avoid admitting that they in fact tionships and families. For example, while physicians of female physicians being the primary or sole income earner are accustomed to their role as experts and expect to be in in their households. In contrast to Protecting and nurturing our intimate relationships may require most physicians experience of medical education, marriage is a re-examination of our professional responsibilities and work non-competitive. John Gottman, a respected re- Does your group discuss shock-absorber systems for searcher in marriage and relationships, stresses the importance parental leaves and urgent family issues? She had speculated that a child would keep geographical triangle: home, school and workplace. Keeping her relationship together, given her partner s attraction to logistics as simple as possible will beneft your marriage and more medicine and achievement. He expresses fear of giving in Raising children together to his feelings lest they derail his career focus. With the For many women physicians, the question of when to plan counsellor s help, they review their priorities with regard childbearing is especially challenging when training demands to career plans and the timing of child-bearing.

Any deformity or complaint of eye pain or vision change after trauma must be fully evaluated isoptin 120 mg cheap blood pressure zero gravity. Signs and symptoms Immediate evaluation as a part of the secondary survey during the trauma work up buy cheap isoptin 40mg line heart attack kush. If yes purchase isoptin 40 mg with visa blood pressure reducers, suggests problem with retinal nerve or stretch of retinal artery o Pupils unequal or one pupil with tear drop shape (no longer round)- if yes, suggests globe rupture or hyphema o Pupils with blood in anterior chamber? Such injuries can crush solid (liver, spleen) and hollow (bowel, stomach) organs against the vertebral spine or pelvis causing significant damage. See table below to help determine which patients to transfer and which to keep and observe. If a pelvic fracture is found there may be additional injuries present in the head, chest, or abdomen. Basic levels include Flex elbows: C6 Extend elbows: C7 Ability to fully abduct little finger (pinky): Tl Motor loss at level of nipples: T4 Motor loss at level of umbilicus: T10 o Motor exam (must be done on all four limbs independently! If wound is from gunshot mark the path of injury by placing a paper clip on the skin at the first wound and a bent paper clip on the second exit wound. Trauma in Pregnancy Definition: Resuscitation is key to decreasing morbidity and mortality in pregnant patients. If the mother needs imaging for diagnosis, shield uterus and perform imaging Management: General goal is to treat mother first as patient. Early Involvement of neonatology for a pregnancy of 28 weeks and above Trauma in Pediatrics Definition: A systematic approach is key to the management of trauma in the pediatric population. Children deteriorate later than adults but once clinical decline begins it is severe and occurs rapidly. Causes Child abuse Road traffic accidents Explosions Blunt or penetrating trauma by animals Fall from height Signs and symptoms History o Ask child what hurts and document symptoms related to injury o Ask family if child is acting normal or has vomiting (head injury) o Has child walked since incident? This means they may not have abdominal pain on exam, but can have significant internal injury o Spinal injury: children have flexible spines and may have spinal cord injury without findings on X-ray Dofullneurologicalexam. Fractures can be classified as open or closed fractures, multi-fragmented (comminuted) or simple and displaced or non-displaced. Fractures most often result from trauma, however occasionally underlying diseases, such as bony malignancy, undermine the strength of the bone such that bone fracture results from minimal trauma. Dislocation refers to a joint dislocation or luxation that occurs when there is an abnormal separation in the joint. The two conditions can co-exist and may be associated with injury of nearby vessels or nerves. Management of Open Fractures Definition: An open fracture refers to the disruption of the skin and underlying soft tissue that results in communication between the fracture and the outside environment. Severity of the open fracture is based on the Gustilo-Anderson Classification: Grade I: The wound is less than lcm long. There is a slight or moderate crushing injury, moderate comminution of the fracture and/or moderate contamination. The choice of antibiotic to be used depends on the fracture type and the likely contamination of the fracture site. Smith fracture Scaphoid and other carpal fractures Scapholunate and perilunate dislocation Distal radio-ulnar dislocation Montaggia fracture Supracondylar fracture Proximal humerus fracture- especially in elderly Clavicle fracture Investigations Labs: none Imaging: X-ray area of tenderness/deformity and joint above and below o Dedicated views may be required: scaphoid fractures Management Distal radius and ulnar fractures o Displaced fractures must be reduced as quickly as possible and splinted with sugar tong splint. Management: The general goal is to assess for associated neurovascular injuries, as they are very common in elbow fractures. Hand Exam and Fractures Definition: Hand fractures can involve any of the 5 metacarpals or 14 phalanges. Fractures of the hand and fingers are commonly accompanied by dislocation or tendon injury. Causes Fall on outstretched hand Direct blow Signs and symptoms Assess for pain, swelling, deformity and limited range of motion Hand examination: o Look: If fingers misaligned consider fracture with rotation or dislocation. Transfer patient for management and include affected limb/digit when possible Placeamputatedsectioningauzesoakedwithsaline, then inside a plastic bag. In hip dislocation, the femoral head may lie anterior (10%) or posterior (90%) to the acetabulum. Delay in repair of certain hip fractures or hip dislocation can lead to avascular necrosis of the femoral head. Long-Bone Fractures of the Leg Definition: Long bone fractures of the lower extremity may affect the tibia, fibula, or femur. Have elevated concern for abuse if the child is not yet ambulatory and has a femur fracture or if the history is not consistent with the type of fracture. Knee Injuries Definition: Knee injuries are common and can be accompanied by significant vascular or neurologic injuries.

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Complications of myocuta- others present with more localised nodularity (see also neous aps include necrosis of the ap and scarring section Breast Lumps isoptin 240 mg without prescription arterial network on the dorsum of the foot, page 409) discount 120mg isoptin overnight delivery arteria magna. Nipple prostheses offer an alternative to ination cheap isoptin 120 mg without a prescription heart attack vol 1 pt 3, imaging and tissue sampling) is required for further surgical treatment. Benign breast disease Fibroadenoma Denition Denition Abnormalities that occur during the normal cycle of Previously broadenomas were considered to be benign breast proliferation and involution. Larger lesions and those with equivocal his- theyarebestconsideredasanaberrationofnormalbreast tology should be excised. Prognosis Incidence Untreated only 10% of broademonas increase in size Most common cause of a discrete breast lump in young over a 2-year period most of which occur in teenage women. Breast cysts Denition Pathophysiology Acommon uid lled epithelial lined space in the breast Fibroadenomas are usually solitary lesions that result presenting as a mass. Fibroadenomas are under hormonal Incidence control,theymayenlargeduringpregnancyandinvolute Palpable cysts occur in 7% of women in Western coun- at menopause. Clinical features Aetiology/pathophysiology Patients (normally young women) present with a Breast cysts are a very common nding in the years lead- smooth, rm, painless nodule that is well-demarcated ing up to the menopause and are thought to arise due to and freely mobile (breast mouse). Juvenile broadenoma is a rare subtype that occurs in femaleadolescentsandgrowsrapidly. Macroscopy/microscopy An encapsulated rubbery white lesion with a glisten- Investigations ing cut surface. It consists of a brous connective tissue Patients require a triple assessment consisting of clinical component and abnormally proliferated ducts and acini examination (see page 409), imaging using ultrasound (adenoma) in varying proportions. Investigations Investigation of any breast lump involves a triple assess- Management ment consisting of clinical examination (see page 409), Patients with a single cyst do not need to be reviewed fol- imaging normally by ultrasound as patients are young lowing an otherwise normal ultrasound and successful and sampling by core biopsy or ne needle aspiration neneedleaspiration. Indications for surgical biopsy in- Management clude bloody uid detected on ne needle aspiration, If conrmed as a broadenoma on triple assessment, aresidual mass following aspiration, or multiple recur- small lesions may be left unless the patient requests rence at the same site. This is Denition associated with an increased risk of developing breast Abenign breast disorder with dilation (ectasia) of the cancer. Clinical features Most patients present with a bloody or serous nipple Age discharge. It is often possible to identify the discharge Most common in women approaching the menopause. There may be a small Aetiology/Pathophysiology swelling at the areolar margin (30%), which if pressed The dilated ducts are lled with inspissated secretions may produce discharge. Macroscopy/microscopy One to two centimetres sized papilloma within a di- Clinical features lated duct with secretions collected behind it. The le- Duct ectasia may be asymptomatic or may cause nipple sion usually consists of fronds of vascular tissue covered discharge (often green) and localised tenderness around byadouble layer of cells resembling ductal epithelium. Investigations Macroscopy/microsopy Mammography and/or ductography show the dilated The ducts may be dilated as much as 1 cm in diam- duct and lling defect. Awire is often passed into the responsible duct, which is excised as a microdochectomy with the breast segment Investigations that drains into it. Although ductography or duc- toscopy are possible, they are not routine investigations. Fat necrosis Denition Management An uncommon condition in which there is death of fat Once the diagnosis is conrmed surgery may be required cellswithin the breast. Treatment is by subareolar excision Aetiology/pathophysiology of the affected ducts. The aetiology is unclear, it is suggested that the death of fat cells may result from trauma. There is an acute inammatory response, which in some cases progresses Duct papilloma to chronic inammation and organisation with brous Denition tissue. The result may be a hard, irregular mass, which Abenign proliferation of the epithelium within large can mimic carcinoma. Clinical features Aetiology pathophysiology Patients present with a hard mass, which may also have Papillomas usually arise less than 1 cm from the nipple skin tethering; often in an obese patient with large and obstruct the natural secretions from the gland. Breast-feeding should be encouraged as this aids drainage of the affected segment of the breast. Lipid-laden macrophages breast-feeding, the baby should be fed from the non- (foam cells/lipophages) may form multinucleate giant infected breast and expression of milk used to drain cells. An alternative is daily ultrasound-guided aspiration with antibiotics until the infection has resolved. Infections of the breast Acute mastitis Breast cancer Denition Acute bacterial inammation of the breast is related to Denition lactation in most cases. Aetiology/pathophysiology r Incidence Breast-feeding predisposes to infection by the devel- Approximately 2/1000 p. Peak 50 60 years Periductal non-lactating mastitis is associated with smoking in 90%. It has been suggested that smok- ing may damage the subareolar ducts, predisposing Sex to infection.

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Due to the routine more material 40mg isoptin for sale blood pressure 170 100, ofen expensive generic isoptin 240 mg fast delivery prehypertension the rationale for early drug therapy, and more efcient character of radionuclide production for nuclear cooling due to higher heat dissipation in the tar- medicine buy isoptin 40mg otc arrhythmia natural cures, economic aspects play an important role get layer. Finally use of a wider energy range may in the choice for a complex solution of a target sys- increase the production of radionuclidic impurities. Te time of bombardment (irradiation time) For a given radionuclide and given production is also strongly related to production costs, since route there are four parameters available to increase cyclotron operation is rather expensive. Example of a multipurpose internal slanted solid target with extremely low angle suitable for production of e. For radionuclides with a half-life signifcantly longer than the irradiation time, the produced activity is almost directly proportional to the irradiation time. Maximisation of the fnal variable, the beam current, is limited by the accelerator performance and by the targetry. Te most widespread are: are directly cooled from the back during process- According to their location with respect to the ing, only the activated layer is etched and used for cyclotron (external or internal). Linear accelera- separation of a radionuclide, and the target can then tors always use external targets. Recently, an interesting varia- examples of internal slanted targets are production tion on liquid targets have attracted the attention systems for 67Ga, 111In, 201Tl or 211At. Tese were success- Modern compact cyclotrons accelerate protons fully used for the pilot production of e. Te shape of the target modify the beam parameters), or located at the end body is very ofen conic in order to compensate for of a beam line whose elements allow for shaping the the gradual increase of the beam diameter due to beam. Te external location enables installation of beam straggling in the gas flling, while minimis- all kinds of target systems, i. Te phase of the target matrix strongly infu- Operation and processing of both liquid and gas ences the target s characteristics. Solid targets are targets can be easily automated, including recycling preferably metallic layers with the best possible of enriched flling. Disassembled external gas target system flled with highly enriched 82Kr for production of 81Rb (top) and its position on an external beam line of the cyclotron U-120M (bottom); a similar target flled with 124Xe is used for production of 123I (Nuclear Physics impurities are opened. Tis cooling efciency and the necessary amount of tar- allows the system to range further from the valley get matrix. Slanted targets (also called tangential of beta-stability thereby forming more exotic radi- or grazing angle targets) are a good choice for solid onuclides. Small angles and higher product yield is accompanied by a reduc- project the beam diameter on a larger target sur- tion in selectivity. In the extreme case of very high face, thereby reducing the heat power per unit of projectile energy (GeV protons) very thick targets area and the target thickness required for optimal (tens of g/cm2) can be irradiated and via fragmen- beam energy loss. Both factors improve cooling tation, spallation and fssion reactions virtually all and increase the maximum applicable beam cur- isotopes from hydrogen up to the target element are rent, especially for target matrices of low thermal produced simultaneously. Cyclotron production of 99mTc wou ld to combine mass separation with chemical separa- require external slanted, high-current targetry that tion to be able to extract single radionuclides. Tis means that only a few reaction channels that potentially contribute to formation of signifcant radionuclidic 3. Te clinical restrictions requiring longer hospitalisation and isola- value and cost-efectiveness of myocardial perfusion tion afer 131I treatment. Deaths from Side efects are mild and reversible and quality-of-life prostate cancer are ofen due to bone disease and of the patients is improved [Kha11]. Te defnition of symptomatic Lymphoma is a blood cancer afecting the white skeletal event covers very serious events such as blood cells. Tese patients with advanced follicular lymphoma that were events are decisive for the quality of life of a cancer either treated by an induction treatment (chemother- patient. Te time to the a comprehensive comparison provided some caution frst symptomatic skeletal event was 15. It is expected that these sumption may difer signifcantly before, during and modifcations could further improve the outcome. Making an assessment of since data from the previous Dose Datamed 1 project possible future trends in radionuclide needs requires (1998-2002) show that Belgium had similar or higher frst of all a comprehensive view of the past and pre- per capita use of nuclear medicine procedures than sent use. Technetium-99m itself issue: if more generators become available more 82Rb is used in more than 80% of diagnostic nuclear will be used (see section 3. Tese applications represent Terapy procedures are still largely dominated approximately 30 million examinations worldwide by 131I for thyroid treatment. Terefore, a weekly 99Mo production of temporal evolution of the use of therapy isotope, about 10. Zevalin hours) and its daughter 99mTc (6 hours), a continu- (90Y-ibritumomab) and 177Lu-rituximab are used for ous supply of 99Mo/99mTc generators to hospitals or treatment of lymphomas. Worldwide radiopharmaceuticals they can be applied in more 99Mo production is presently being converted from hospitals and more countries.

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Particular attention must be A frst-year resident working in a major urban hospital paid to certain types of relationships and power imbalances is fve months pregnant when she does her rotation and [ ] such as attending physician and resident discount isoptin 240mg without a prescription blood pressure chart heart rate, resident and fnds that the nurses are very kind to her proven isoptin 40 mg blood pressure medication drug test. One night Murray Goldstein states this idea more simply [c]ollegiality while she is on call a woman in labour begins to show signs requires a fostering of the attitude we are in this together discount isoptin 240mg on-line pulse pressure tachycardia. The nurse looks at her and The advantages of good relationships among members of a leaves the room without responding. The nurse returns the benefts are improved care to patients and improved patient with the fellow and starts to explain the patient s situation. The open sharing of information, and the attitude that The fellow notes that she is in the appropriate position and questioning and checking is expected, leads to safer care. The resident is astonished that the nurse ignored error or a nurse, acting on previous experience with a patient, her request and yet is willing to run to obtain things for the to question an order for a medication to which she believes fellow. Patients also report improved satisfaction in her relationship with the nurse and feels angry that her with care when members of the team work together. Both physicians and nurses who work on well-functioning Introduction teams report improved work satisfaction, less burnout, im- The culture of health care has changed over the past few proved morale, increased motivation and reduced confict. Well-functioning teams have great professional relationships and good communication with con- potential in delivering excellent patient care and improving sultants and other members of the multidisciplinary team, as patient safety. Poorly functioning teams, particularly those one of the most signifcant factors in improving the resilience with communication problems, can present signifcant risks of physicians. The ability to establish collegial relationships with members of the health care team is essential. Given the many benefts of collegiality, it is important to ad- Physicians must not only work with other health professionals dress potential barriers to good working relationships. Bulgar in a collegial fashion but must also establish good relation- and Bulgar highlight problems that subspecialists encounter in ships with clinicians and faculty members in other specialties. For their part, family phy- Collegiality enables academic interchange and collaboration at sicians frequently point to disparaging comments made about the level of the individual case, in the development of new them by specialist colleagues. We forget that it is impossible if techniques for medical care, and in research activities, improv- not futile to expect one physician to acquire a good working ing outcomes in all of these spheres. It can also be diffcult to be respectful of others when service demands are high, time is short, and we are fatigued from being on call. In an exploration of professional relationships Take the lead in fostering the idea that we are between nurses and physicians, Zelek and Phillips found that all in this together. Smith argue that while assertive nurses resent being put down by doctors, physicians resent being challenged by nurses. Summary Improving interprofessional collegiality Health care has rapidly evolved and is now delivered by teams It is only common sense that treating others with respect will of professionals. Physicians for whom this is a shift in their ac- improve relationships and improve team communication and customed practise style will beneft from refecting on the role effectiveness. Achieving this, however, can be more com- they have with a team of fellow health practitioners. The perception of ownership: this can include perceived After the resident speaks to the fellow about the situation, ownership of specialized knowledge, technical skills, the fellow offers to speak to the nurse on her behalf. The equipment, clinical territory and even the patient himself resident wanted to deal with this herself so waited until or herself. For example, a nurse described her frustration she and the nurse were alone and raised the issue with the when residents rely on her assessment but when presenting nurse. The resident told the nurse she was surprised and at rounds make it sound as if they have done the assess- angry when her request was ignored and was concerned ment themselves. Trade can be in concrete haviour but did say she saw the resident as one of them physical commodities such as equipment and beds, but it and not as a physician to take charge in an emergency. When they get respect they exchange it for information, knowledge, The resident begins to question her friendliness with the resources and goodwill. Failure to give respect can be met nursing staff and wondered if she needed to set herself with revenge strategies in the form of an embargo of apart from them but decided that she would keep talking trade. Although many sources call for clear policies and procedures so that roles on the team are clear, there are also more subtle Key references rules of the game that will never appear in a manual. The rules resident stated it like this: Your name can be ruined or made of the game: interprofessional collaboration on the intensive on one encounter you have to be very careful, because if you care unit team. The hierarchical model of care that was ac- The doctor whose patient is a physician faces particular chal- cepted in the past is outmoded in today s patient-centred health lenges. The fundamental principles of the Canadian naturally relate to the patient as a peer, as well as in the role of Medical Association s Code of Ethics emphasize that the doctor. The patient may be a close colleague, such as a clinician physician is to [f]irst consider the well-being of the patient in the department. They may be a distant acquaintance, but one and to [p]ractice the profession of medicine in a manner who sits on the same board meetings or on the same hospital that treats the patient with dignity and as a person worthy of medical advisory committee.

Box 52 Secondary author performing more than one role If the same secondary author performs more than one role: List all the roles in the order they are given Separate the roles by "and" End secondary author information with a period Example: Jones buy generic isoptin 40mg online blood pressure medication plendil, Albert B order 240mg isoptin with amex blood pressure ideal. Box 53 Non-English names for secondary authors Translate the word found for editor proven isoptin 40mg arteria elastica, translator, illustrator, or other secondary author into English whenever possible. Manuscript collection with author and compiler Date for Manuscript Collections (required) General Rules for Date Give the date range of the items in the collection Enter the earliest date of the items in the collection, a hyphen, and the latest date of the items. 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Intuitively purchase isoptin 40 mg fast delivery arteria auricular posterior, there are so many immunes that the average infective cannot replace itself with at least one new infective during the infectious period and order isoptin 120mg with amex arrhythmia symptoms in children, consequently generic isoptin 240mg with mastercard pulse pressure ejection fraction, the disease dies out. If the inequality above is not satised and there are some infecteds initially, then we expect the susceptible fraction to approach the stable age distribution given by the jump solution with a positive, constant that satises (5. The negative signs in the expression for A make it seem as if A is a decreasing function of the successfully vaccinated fraction g, but this is not true since the force of infection is a decreasing function of g. For the demo- graphic model in which everyone survives until age L and then dies, d(a) is zero until age L and innite after age L, so that D(a) is zero until age L and is innite after age L. Expressions similar to those in this section can be found for a nonconstant population with = q/(1 eqL), but they are not presented here. Typically the lifetime L is larger than the average age of attack A 1/, and both are much larger than the average latent period 1/ and the average infectious period 1/. Hence many of the formulas for 0 0 Type I mortality in the Anderson and May book [12, Ch. In sections 7 and 8 we estimate the basic reproduction number in models with age groups for measles in Niger and pertussis in the United States. The boundary values at age 0 are all zero except for the births given by S(0,t)= 0 f(a)U(a, t)da. The population is partitioned into n age groups as in the demographic model in section 4. Because the numbers are all growing exponentially by eqt, the fractions of the population in the epidemiologic classes are of more interest than the numbers in these epidemiologic classes. Here we follow the same procedure used in the continuous model to nd an expression for the basic re- production number R0. Substituting s successively, we nd that s = C /[ ] 1 1 1 i1 i i1 i 1 for i 2, where Ci1 stands for ci1 c1c1P1. When the expressions for ei and ii1 are substituted into the expression for i in (6. Now the expressions for i and = kb can be substituted into this j=1 j j i i i last summation to obtain n j bj bj1 b1 (6. Here the feasible region is the subset of the nonnegative orthant in the 4n-dimensional space with the class fractions in the ith group summing to Pi. Using s P, n n n j1 j1 j j1 j1 n1 1 i i we obtain V (R 1) b i 0ifR 1. The set where V = 0 is the boundary of 0 j j 0 the feasible region with ij = 0 for every j, but dij/dt = jej on this boundary, so that ij moves o this boundary unless ej = 0. Thus the disease-free equilibrium is the only positively invariant subset of the set with V = 0, so that all paths in the feasible region approach the disease-free equilib- rium by the Liapunov Lasalle theorem [92, p. Thus if R0 1, then the disease- free equilibrium is asymptotically stable in the feasible region. If R0 > 1, then we have V> 0 for points suciently close to the disease-free equilibrium with s close to P and i i ij > 0 for some j, so that the disease-free equilibrium is unstable. A deterministic compartmental mathemati- cal model has been developed for the study of the eects of heterogeneous mixing and vaccination distribution on disease transmission in Africa [133]. This study focuses on vaccination against measles in the city of Naimey, Niger, in sub-Saharan Africa. The rapidly growing population consists of a majority group with low transmission rates and a minority group of seasonal urban migrants with higher transmission rates. De- mographic and measles epidemiological parameters are estimated from data on Niger. The fertility rates and the death rates in the 16 age groups are obtained from Niger census data. From measles data, it is estimated that the average period of passive immunity 1/ is 6 months, the average latent period 1/ is 14 days and the average infectious period 1/ is 7 days. From data on a 1995 measles outbreak in Niamey, the force of infection is estimated to be the constant 0. A computer calculation using the demographic and epidemiological parameter values in the formula (6. Recall from section 1 that the replacement number R is the actual number of new cases per infective during the infectious period. R can be approximated by computing the sum over all age groups of the daily incidence times the average infectious period times the fraction surviving the latent period, and then dividing by the total number of infectives in all age groups, so that 16 1 j=1jsjPj + dj + q + dj + q R =. This contact number is approximated by computing the product of the sum of the daily incidences when all contacts are assumed to be with susceptibles times the average infectious period, and dividing by the total number of infectives. The average age of infection can be approximated in the measles computer simulations by the quotient of the sum of the average age in each age group times the incidence in that age group and the sum of the incidences. This model is plausible because the age distribution of the Niger population is closely approximated by a negative exponential [133]. Using this d value and the fertilities in the Lotka characteristic equation for discrete age groups (4.