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1.
Rheumatol Int ; 2024 Aug 13.
Artículo en Inglés | MEDLINE | ID: mdl-39136784

RESUMEN

In recent years Janus kinase inhibitors (JAKi) have joined tumor necrosis factor inhibitors (TNFi) and interleukin (IL)-17 inhibitors (IL-17i) as approved disease modifying anti-rheumatic drugs (DMARD) for moderate to severe forms of axial spondyloarthritis (axSpA). Drug survival in axSpA patients has not been well studied in a real-world outpatient scenario since the approval of JAKi. We aimed to analyze the three drug classes based on modes of actions (MoA) for their persistence rates among German axSpA outpatients. A retrospective analysis of the RHADAR database for axSpA patients with a new initiation of TNFi, IL-17i, or JAKi treatment between January 2015 and October 2023 was conducted. Analyses included Kaplan-Meier curves and adjusted Cox regressions for drug discontinuation. 1222 new biological DMARD (TNFi [n = 954], IL-17i [n = 190]) or JAKi (n = 78) treatments were reported. The median drug survival was 31 months for TNFi, 25 for IL-17i, and 18 for JAKi. The corresponding 2-year drug survival rate was 79.6%, 72.6%, and 62.8% for TNFi, IL-17i, and JAKi, respectively. The probability for discontinuation for JAKi was significantly higher compared with TNFi (HR 1.91 [95% CI 1.22-2.99]) as well as for IL-17i compared with TNFi (HR 1.43 [95% CI 1.02-2.01]), possibly related to more frequent use of TNFis as first-line therapy. IL-17i and JAKi discontinuation probabilities were similar. Primary non-response was the reason for drug discontinuation in most cases across all MoA. TNFi treatment might persist longer than JAKi and IL-17i in German axSpA outpatients, possibly related to more severe or refractory disease in patients with JAKi-treated or IL-17i-treated axSpA.

2.
Front Immunol ; 15: 1395968, 2024.
Artículo en Inglés | MEDLINE | ID: mdl-38846940

RESUMEN

Objective: Treatment options with disease-modifying antirheumatic drugs (DMARDs) for psoriatic arthritis (PsA) have evolved over recent years. In addition to Janus kinase inhibitors (JAKi), four classes of biologic DMARDs (bDMARDs; interleukin [IL]-23 inhibitors [IL-23i], IL-12/23 inhibitors [IL-12/23i], tumor necrosis factor inhibitors [TNFi], and IL-17 inhibitors [IL-17i]) are currently approved for moderate to severe PsA treatment. There is minimal evidence of the persistence of these drugs among PsA outpatients in a real-world scenario during the period following the approval of JAKi. Therefore, we aimed to analyze the drug survival rates of biologic and JAKi therapies among German PsA outpatients during routine clinical care. Methods: We retrospectively analyzed PsA patients with a new prescription for a biologic or JAKi in the RHADAR database between January 2015 and October 2023. Kaplan-Meier Curves and Cox regression modelling were used to compare drug survival rates. Results: 1352 new prescriptions with bDMARDs (IL-12/23i [n=50], IL-23i [n=31], TNFi [n=774], IL-17i [n=360]) or JAKi (n=137) were identified. The 5-year drug survival rate was 67.8% for IL-17i, 62.3% for TNFi, 53.3% for JAKi, and 46.0% for IL-12/23i. Discontinuation probabilities for JAKi and IL-12/23i were significantly higher compared with TNFi (JAKi hazard ratio [HR] 1.66, [95% CI 1.23-2.24], p=0.001; IL-12/23i HR 1.54, [95% CI 1.02-2.33], p=0.042) and IL-17i (JAKi HR 1.77, [95% CI 1.27-2.47], p=0.001; IL-12/23i HR 1.64, [95% CI 1.06-2.55], p=0.027). JAKi-treated patients had more severe disease and more osteoarthritis (OA) compared to TNFi and more OA compared to IL-17i. Conclusion: German PsA outpatients might persist longer with TNFi and IL-17i compared with IL-12/23i or JAKi. For TNFi, differences in subgroup characteristics and comorbidities (OA) may have affected drug survival rates. For IL-17i, the longer drug survival might not only be related to less OA compared to JAKi and, therefore, might be affected by other factors.


Asunto(s)
Antirreumáticos , Artritis Psoriásica , Interleucina-12 , Interleucina-17 , Interleucina-23 , Inhibidores de las Cinasas Janus , Humanos , Artritis Psoriásica/tratamiento farmacológico , Artritis Psoriásica/mortalidad , Masculino , Femenino , Estudios Retrospectivos , Persona de Mediana Edad , Interleucina-17/antagonistas & inhibidores , Alemania , Interleucina-12/antagonistas & inhibidores , Interleucina-23/antagonistas & inhibidores , Inhibidores de las Cinasas Janus/uso terapéutico , Antirreumáticos/uso terapéutico , Adulto , Inhibidores del Factor de Necrosis Tumoral/uso terapéutico , Anciano , Bases de Datos Factuales , Pacientes Ambulatorios , Resultado del Tratamiento
3.
Rheumatol Int ; 44(4): 653-661, 2024 Apr.
Artículo en Inglés | MEDLINE | ID: mdl-37805981

RESUMEN

The categorization of axial spondyloarthritis (axSpA) into radiographic (r-axSpA) and non-radiographic (nr-axSpA) subtypes is important in clinical trials but may be of less value in clinical practice. This exploratory cross-sectional, multi-center study evaluated patients with axSpA under routine care at German clinical rheumatology sites (RHADAR real-world database), with a focus on imaging data used for diagnostic classifications. Our analyses included 371 patients with axSpA. The mean (standard deviation [SD]) age was 50.9 (14.0) years, disease duration was 16.4 (13.5) years, and 39.6% were female. Based on the rheumatologist's final assessment, almost half of patients had definite r-axSpA (n = 179; 48.2%), 53 (14.3%) had suspected r-axSpA, 112 (30.2%) had non-radiographic-axSpA (nr-axSpA), and 27 (7.3%) had undefined axSpA. Patients assessed with definite or suspected r-axSpA were more likely to be treated with disease-modifying antirheumatic drugs (DMARDs) (62.0% and 64.2%, respectively) compared with nr-axSpA or undefined axSpA patients (37.5% and 48.1%, respectively). Almost all patients (348/371; 93.8%) had sacroiliac joint imaging data (radiographs or magnetic resonance imaging) documented in their charts, but only 216 (58.2%) had conventional radiographs required for formal diagnosis of r-axSpA by modified New York criteria. Follow-up radiographic imaging in nr-axSpA patients was uncommon (23/216 [25.0%]) but confirmed r-axSpA in 9/23 patients (39.1%). In conclusion, radiographs were available for slightly more than half of axSpA patients. Follow-up imaging was infrequent during rheumatology care in Germany but confirmed r-axSpA in ~ 40% of patients originally considered to have nr-axSpA. The distinction between r-axSpA and nr-axSpA may be ill-defined in routine clinical practice.


Asunto(s)
Antirreumáticos , Espondiloartritis Axial no Radiográfica , Reumatología , Espondiloartritis , Espondilitis Anquilosante , Humanos , Femenino , Persona de Mediana Edad , Masculino , Espondiloartritis/diagnóstico por imagen , Espondiloartritis/tratamiento farmacológico , Estudios Transversales , Espondilitis Anquilosante/tratamiento farmacológico , Antirreumáticos/uso terapéutico
4.
Rheumatol Int ; 43(1): 89-97, 2023 01.
Artículo en Inglés | MEDLINE | ID: mdl-36441274

RESUMEN

Spondyloarthritis may contribute to deficits in cognition. The objective of this study was to compare cognitive abilities in patients with axial spondyloarthritis (axSpA) or psoriatic arthritis (PsA) with matched reference groups. This investigator-initiated, cross-sectional, exploratory study of adults with axSpA or PsA was conducted at two German rheumatology centres (November 2018-September 2019). All data on patient and disease characteristics and cognitive abilities were collected at a single visit. Cognitive function was assessed by the previously validated Memory and Attention Test subscores of selective attention, episodic working memory, and episodic short-term memory and compared with subscores from healthy age-, sex-, and education-matched reference subjects. The mean patient age was 51.1 and 55.8 years in the axSpA (n = 101) and PsA (n = 117) groups, respectively, and mean symptom duration was 13.7 and 10.3 years. Compared with matched reference subjects, axSpA and PsA patients showed significant impairments in selective attention (mean difference of -6.5 and -4.5, respectively, on a 45-point scale; P < 0.001 for both) and no significant differences in episodic working memory. The PsA cohort, but not the axSpA cohort, had significantly better episodic short-term memory subscores compared with matched reference subjects (mean change of 2.0 on a 15-point scale; P < 0.001). Explorative subgroup analyses were unable to identify factors influencing cognitive changes, including disease activity, pain, and function, but may have been underpowered. We conclude that impairments in selective attention may impact the ability of axSpA and PsA patients to process information. These findings warrant additional studies, including longitudinal analyses, in patients with spondyloarthritis.


Asunto(s)
Artritis Psoriásica , Espondiloartritis Axial , Espondiloartritis , Espondilitis Anquilosante , Adulto , Humanos , Persona de Mediana Edad , Artritis Psoriásica/complicaciones , Artritis Psoriásica/diagnóstico , Espondilitis Anquilosante/diagnóstico , Estudios Transversales , Espondiloartritis/complicaciones , Espondiloartritis/diagnóstico , Espondiloartritis/psicología , Cognición
5.
Front Med (Lausanne) ; 8: 748262, 2021.
Artículo en Inglés | MEDLINE | ID: mdl-34790678

RESUMEN

This longitudinal analysis compares the prevalence of depressive symptoms in patients with psoriatic arthritis in the context of the COVID-19 pandemic. Data from a national patient register in Germany were analyzed regarding the Patient Health Questionnaire 2 (PHQ-2) to identify cases suspicious for depression at two time points, i.e., before and during the COVID-19 pandemic. Only patients with complete concurrent information on the Disease Activity in Psoriatic Arthritis Score (DAPSA) were included in the analysis. The frequency of depressive symptoms in psoriatic arthritis patients during the COVID-19 pandemic did not differ from the prevalence rates measured before. In addition, prevalence rates for depressive symptoms did not differ when stratifying the patient sample for DAPSA levels of disease activity measured before the pandemic. These results were confirmed further in a sensitivity analysis, limiting the second PHQ-2 assessment to lockdown periods only. However, longitudinal data on the prevalence of depressive symptoms in patients with rheumatic diseases, in general, and psoriatic arthritis, in particular, are scarce in the context of the COVID-19 pandemic. For a sensible comparison of prevalence rates for depressive symptoms in the future, underlying SARS-CoV-2 infection rates and resulting local healthcare disruptions need to be taken into account, besides the potential use of different depression screening tools to evaluate resulting numbers sensibly and draw corresponding conclusions for patient care.

6.
J Med Internet Res ; 23(5): e28164, 2021 05 20.
Artículo en Inglés | MEDLINE | ID: mdl-34014170

RESUMEN

Real-world data are crucial to continuously improve the management of patients with rheumatic and musculoskeletal diseases (RMDs). The German RheumaDatenRhePort (RHADAR) registry encompasses a network of rheumatologists and researchers in Germany providing pseudonymized real-world patient data and allowing timely and continuous improvement in the care of RMD patients. The RHADAR modules allow automated anamnesis and adaptive coordination of appointments regarding individual urgency levels. Further modules focus on the collection and integration of electronic patient-reported outcomes in between consultations. The digital RHADAR modules ultimately allow a patient-centered adaptive approach to integrated medical care starting as early as possible in the disease course. Such a closed-loop system consisting of various modules along the whole patient pathway enables comprehensive and timely patient management in an unprecedented manner.


Asunto(s)
Enfermedades Musculoesqueléticas , Enfermedades Reumáticas , Reumatología , Alemania , Humanos , Sistema de Registros
7.
J Toxicol Environ Health A ; 80(7-8): 411-416, 2017.
Artículo en Inglés | MEDLINE | ID: mdl-28696914

RESUMEN

The gold standard of saving fresh tissue in liquid nitrogen has some serious disadvantages in that this process is not available in daily medical routine practices even in many tumor centers. Our approach of a new minimally invasive technique is obtaining urothelial cells via micro-brushing the urinary bladder on the occasion of urological routine methods such as transurethral resection (TUR). Urothelial cells were obtained from 25 patients via two different micro-brushes from tumor tissue and from macroscopically healthy tissue during TUR. These cells were immediately transferred into RNA stabilization reagent and stored at -20°C. Later, mRNA was isolated, transcribed into cDNA, and amplified. cDNA was stored at -20°C until analysis. The mean RNA quantity was 99.5 ng/µl from tumor tissues and 66.3 ng/µl from macroscopically tumor-free tissue, enabling a considerable number of analyses. The quality of the gained cDNA allowed semi-quantitative PCR analysis of GSTM1 expression as well as quantitative PCR analysis of c-Myc expression. The new technique presents several important advantages. First, staging and grading of the stained tumor sample can be examined immediately, whereas fresh frozen sample is not examined until some days later. Further, this method can be applied in hospitals with no access to liquid nitrogen or without capability to provide an additional examination of frozen tumor sample by a pathologist. This presented minimally invasive method enables investigation of gene expression in the urinary bladder without disadvantages of the need for storage of fresh tissues in liquid nitrogen.


Asunto(s)
Perfilación de la Expresión Génica/métodos , Neoplasias de la Vejiga Urinaria/fisiopatología , Vejiga Urinaria/citología , Urotelio/citología , ADN Complementario/análisis , Humanos
8.
Appl Environ Microbiol ; 81(9): 3039-48, 2015 May 01.
Artículo en Inglés | MEDLINE | ID: mdl-25710366

RESUMEN

Plant pathogens cause major economic losses in the agricultural industry because late detection delays the implementation of measures that can prevent their dissemination. Sensitive and robust procedures for the rapid detection of plant pathogens are therefore required to reduce yield losses and the use of expensive, environmentally damaging chemicals. Here we describe a simple and portable system for the rapid detection of viral pathogens in infected plants based on immunofiltration, subsequent magnetic detection, and the quantification of magnetically labeled virus particles. Grapevine fanleaf virus (GFLV) was chosen as a model pathogen. Monoclonal antibodies recognizing the GFLV capsid protein were immobilized onto immunofiltration columns, and the same antibodies were linked to magnetic nanoparticles. GFLV was quantified by immunofiltration with magnetic labeling in a double-antibody sandwich configuration. A magnetic frequency mixing technique, in which a two-frequency magnetic excitation field was used to induce a sum frequency signal in the resonant detection coil, corresponding to the virus concentration within the immunofiltration column, was used for high-sensitivity quantification. We were able to measure GFLV concentrations in the range of 6 ng/ml to 20 µg/ml in less than 30 min. The magnetic immunoassay could also be adapted to detect other plant viruses, including Potato virus X and Tobacco mosaic virus, with detection limits of 2 to 60 ng/ml.


Asunto(s)
Separación Inmunomagnética/métodos , Nepovirus/aislamiento & purificación , Enfermedades de las Plantas/virología , Carga Viral/métodos , Nanopartículas/química , Potexvirus/aislamiento & purificación , Factores de Tiempo , Virus del Mosaico del Tabaco/aislamiento & purificación
9.
Comput Math Methods Med ; 2012: 784512, 2012.
Artículo en Inglés | MEDLINE | ID: mdl-23424603

RESUMEN

This paper presents the modeling of a host immune system, more precisely the immune effector cell and immune memory cell population, and its interaction with an invading pathogen population. It will tackle two issues of interest; on the one hand, in defining a stochastic model accounting for the inherent nature of organisms in population dynamics, namely multiplication with mutation and selection; on the other hand, in providing a description of pathogens that may vary their antigens through mutations during infection of the host. Unlike most of the literature, which models the dynamics with first-order differential equations, this paper proposes a Galton-Watson type branching process to describe stochastically by whole distributions the population dynamics of pathogens and immune cells. In the first model case, the pathogen of a given type is either eradicated or shows oscillatory chronic response. In the second model case, the pathogen shows variational behavior changing its antigen resulting in a prolonged immune reaction.


Asunto(s)
Sistema Inmunológico , Infecciones/microbiología , Infecciones/parasitología , Infecciones/virología , Informática Médica/métodos , Algoritmos , Animales , Evolución Biológica , Humanos , Linfocitos/inmunología , Modelos Inmunológicos , Modelos Estadísticos , Dinámica Poblacional , Probabilidad , Procesos Estocásticos
10.
J Mol Model ; 18(2): 607-9, 2012 Feb.
Artículo en Inglés | MEDLINE | ID: mdl-21559961

RESUMEN

The concept called Knowledge is a measure of the quality of genetically transferred information. Its usefulness is demonstrated quantitatively in a Monte-Carlo simulation on critical steps in a origin of life model. The model describes the origin of a bio-like genetic apparatus by a long sequence of physical-chemical steps: it starts with the presence of a self-replicating oligomer and a specifically structured environment in time and space that allow for the formation of aggregates such as assembler-hairpins-devices and, at a later stage, an assembler-hairpins-enzyme device-a first translation machine.


Asunto(s)
Método de Montecarlo , Origen de la Vida , Simulación por Computador , Ambiente , Humanos , Modelos Teóricos , Proteínas , ARN
11.
Skin Res Technol ; 15(2): 161-7, 2009 May.
Artículo en Inglés | MEDLINE | ID: mdl-19622125

RESUMEN

BACKGROUND: The quality and extent of leg ulcer healing in deeper skin layers remains poorly defined using standard visual inspection alone. High-resolution ultrasound (HR-US) offers a non-invasive, quantitative and objective assessment of dimensional and structural changes deep within the wound. METHODS: In a prospective, single-center study, healing of chronic, treatment-resistant leg ulcers was monitored by standard photography and HR-US. RESULTS: Twenty patients with 22 ulcers were enrolled. After study entry, treatment comprised continuation of conventional management (n=4) or application of Apligraf (n=17) or Thiersch (n=1). All ulcers receiving a graft were classified as 'clinically healed' by visual inspection within a maximum of 5 weeks. With conventional management, closure required a period of several months in three out of four cases. After covering the ulcer with Apligraf, the skin reconditioned, resulting in fair skin color and a smooth skin surface in all but one case. HR-US images, however, revealed large subepidermal deficits of elastic and collagenous fibers at the time of 'clinical healing' in 14/18 engrafted ulcers, findings that are strongly indicative of a weakened skin scaffolding. CONCLUSION: We suggest that the healing process for chronic ulcers can be monitored with both standard visual inspection (photography) and HR-US to allow early intervention.


Asunto(s)
Dermoscopía/métodos , Aumento de la Imagen/métodos , Úlcera de la Pierna/patología , Úlcera de la Pierna/terapia , Ultrasonografía/métodos , Cicatrización de Heridas , Adulto , Femenino , Humanos , Masculino , Estudios Prospectivos , Resultado del Tratamiento , Adulto Joven
12.
Clin Interv Aging ; 3(1): 175-82, 2008.
Artículo en Inglés | MEDLINE | ID: mdl-18488887

RESUMEN

In this prospective design study the effects of low-energy partially focused extracorporeal generated shock waves (ESW) onto a subcutaneous located varicose vein - left vena saphena magna (VSM)- are investigated. The treatment consisted of 4 ESW applications within 21 days. The varicose VSM of both sides were removed by surgery, and samples analyzed comparing the treated and untreated by means of histopathology. No damage to the treated varicose vein in particular and no mechanical destruction to the varicose vein's wall could be demonstrated. However, an induction of neo-collagenogenesis was observed. The thickness of the varicose vein's wall increased. Optimization of critical application parameters by investigating a larger number of patients may turn ESW into a non-invasive curative varicose treatment.


Asunto(s)
Ondas de Choque de Alta Energía/uso terapéutico , Várices/terapia , Matriz Extracelular , Humanos , Pletismografía , Várices/patología , Venas/efectos de la radiación
13.
Clin Interv Aging ; 3(1): 201-10, 2008.
Artículo en Inglés | MEDLINE | ID: mdl-18488890

RESUMEN

In this case study of an unique instance, effects of medium-energy, high-focused extracorporeal generated shock waves (ESW) onto the skin and the underlying fat tissue of a cellulite afflicted, 50-year-old woman were investigated. The treatment consisted of four ESW applications within 21 days. Diagnostic high-resolution ultrasound (Collagenoson) was performed before and after treatment. Directly after the last ESW application, skin samples were taken for histopathological analysis from the treated and from the contra-lateral untreated area of skin with cellulite. No damage to the treated skin tissue, in particular no mechanical destruction to the subcutaneous fat, could be demonstrated by histopathological analysis. However an astounding induction of neocollageno- and neoelastinogenesis within the scaffolding fabric of the dermis and subcutis was observed. The dermis increased in thickness as well as the scaffolding within the subcutaneous fat-tissue. Optimization of critical application parameters may turn ESW into a noninvasive cellulite therapy.


Asunto(s)
Ondas de Choque de Alta Energía , Lipodistrofia/terapia , Grasa Subcutánea/efectos de la radiación , Femenino , Humanos , Lipodistrofia/patología , Persona de Mediana Edad , Estudios Prospectivos , Piel/patología , Piel/efectos de la radiación
14.
Clin Interv Aging ; 2(4): 623-30, 2007.
Artículo en Inglés | MEDLINE | ID: mdl-18225463

RESUMEN

The present study investigates the effects of low-energy defocused extracorporeal generated shock waves on collagen structure of cellulite afflicted skin. Cellulite measurement using high-resolution ultrasound technology was performed before and after low-energy defocused extracorporeal shock wave therapy (ESWT) in 21 female subjects. ESWT was applied onto the skin at the lateral thigh twice a week for a period of six weeks. Results provide evidence that low-energy defocused ESWT caused remodeling of the collagen within the dermis of the tested region. Improving device-parameters and therapy regimes will be essential for future development of a scientific based approach to cellulite treatment.


Asunto(s)
Tejido Adiposo , Obesidad/terapia , Terapia por Ultrasonido , Adulto , Femenino , Humanos , Persona de Mediana Edad , Suiza
15.
J Biol Phys ; 32(6): 563-72, 2006 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-19669442

RESUMEN

UNLABELLED: A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. FIRST CASE: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N individuals of the mutant W(n)(S)(N) after the multiplication phase M of the n-th generation (with probability delta of an error in the replication, where all possible errors are fatal errors) and W(n)(S)(N) after the following selection phase S (with probability beta that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction W(infinity)(S)(0) are obtained. Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N(p) individuals of the primary mutant and N(m) individuals of the new form W(n)(M)(N(p), N(m)) after the multiplication phase M of the n-th generation (probability varepsilon of an error in the replication of the primary mutant giving the new form) and W(n)(S)(N(p), N(m) after the following selection phase S (probabilities beta(p) and beta(m) that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained.

16.
J Biol Phys ; 31(3-4): 571-85, 2005 Dec.
Artículo en Inglés | MEDLINE | ID: mdl-23345919

RESUMEN

Evolution is assumed to begin in a very particular compartmentalized location with periodic conditions. A highly diversified world is the driving force for the continuous increase in complexity by colonizing increasingly less favourable regions. Modeling the "origin-of-life" a Darwinian cyclic process is simulated (multiplication with sporadic errors followed by a construction and selection).Starting from a RNA-world (R-strands of R(1) and R(2) monomers building Hairpin-Assembler devices) and introducing another kind of monomers (A(1) and A(2) which interlink to the Hairpin-Assembler devices such that they become bound and form an A-oligomer) it is shown that a simple translation apparatus evolves producing enzymes (specific sequences of A(1) and A(2) monomers given by the sequences of R(1) and R(2) monomers on the assembler-strands). Later on D-strands are introduced, which are not capable of participating in the synthesis of A-oligomers. These D-strands become carriers of the genetic information and induce the formation of increasingly complex entities of functionally interplaying components.

17.
J Biol Phys ; 31(3-4): 587-97, 2005 12.
Artículo en Inglés | MEDLINE | ID: mdl-23345920

RESUMEN

UNLABELLED: A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. FIRST CASE: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N mutants W(n) (M)(N) after the multiplication phase M of the n-th generation (with probability δ of an error in the replication, where all possible errors are fatal errors) and W(n) (S)(N) after the following selection phase S (with probability ß that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction W(∞) (S)(0) are obtained.Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N(p) primary mutants and N(m) of the new form W(n) (M)(N(p), N(m)) after the multiplication phase M of the n-th generation (probability ε of an error in the replication of the primary mutant giving the new form) and W(n) (S)(N(p), N(m)) after the following selection phase S (probabilities ß(p) and ß(m) that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained.

18.
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