On threshold dynamics for periodic and time-delayed impulsive systems and application to a periodic disease model

<abstract><p>The basic reproduction ratio $ \mathcal{R}_{0} $ of more general periodic and time-delayed impulsive model which the period of model coefficients is different from that of fixed impulsive moments, is developed. That $ \mathcal{R}_{0} $ is the threshold parameter for the stability of the zero solution of the associated linear system is also shown. The developed theory is further applied to a swine parasitic disease model with pulse therapy. Threshold results on its global dynamics in terms of $ \mathcal{R}_{0} $ are obtained. Some numerical simulation results are also given to support our main results.</p></abstract>

Cases of Periodic Disease (Familial Mediterranean fever) among Dagestan Republic population

The article represents a brief overwiev of current understanding concerning Periodic Disease (Familial Mediterranean fever). There are some recommendations for diagnostics and modern treatment with the use of Colchicine, as a protection from kidney amyloidosis development. Materials are based on the analysis of our own clinical data.

FAMILIAL MEDITERRANEAN FEVER. THE PRESENT-DAY VIEW OF THE PROBLEM. MANIFESTATIONS OF MAXILLOFACIAL AREA

Periodic disease - hereditary disease spreaded among the ancient peoples of the Mediterranean coast. The questionnaire and retrospective analysis of manifestations of periodic disease for patients living in the Russian Federation was composed in the child-maxillofacial department of the MSMSU named after A.I. Evdokimov. The research of medical histories of patients let us notice that every patient needs individual treatment and prophylaxis of frequent attacks. Nowadays Russian pediatricians are poorly informed about the periodic disease. As a consequence, we have detected a large number of mistakes in the diagnosis.

A CASE OF LATE DIAGNOSIS OF FAMILIAL MEDITERRANEAN FEVER COMPLICATED BY AA-AMYLOIDOSIS

The aimof study was to describe a clinical case of a hereditary disease with autosomal recessive type of inheritance – familial Mediterranean fever (FMF).Materials and methods.Patient A., 19 years old, Armenian, was hospitalized in the Department of rheumatology of the clinical hospital with complaints of periodic temperature rises to 39 °C, paroxysmal pain in the abdomen, ankle and hip joints, legs edema. In anamnesis from 8 months of age there were attacks of 1–2 day abdominal pain in combination with febrile fever; from 2 years there were arthralgia of the ankle joints, followed by knee and hip. Attacks of fever and joint syndrome recurred 3–4 times a year, lasted for 2–3 days, and disappeared spontaneously. Treatment with nonsteroidal anti-inflammatory drugs and small doses of prednisone was carried out. The examination in the hospital revealed nephrotic syndrome without impaired renal function, increasing of erythrocyte sedimentation rate (up to 62 mm/h), C-reactive protein (up to 60 mg/dl), leukocytosis (up to 16.7 × 109/L). The immunological examination revealed no abnormalities. Bacteriological and serological studies have ruled out the possibility of infectious diseases. Electrocardiography, echocardiography, ultrasound of abdomen and kidneys, multispiral computed tomography of kidneys and retroperitoneum, magnetic resonance imaging of the sacroiliac joints, nephrobiopsy were performed.Results.During the examination, a wide differential diagnosis with infectious and rheumatic diseases was carried out. Taking into account the polysyndromicity of clinical manifestations, systemic lupus erythematosus was suggested. An induction course of immunosuppressive therapy was conducted, that was ineffective. The diagnosis of systemic lupus erythematosus was doubtful and to clarify the nature of kidney morphological changes nephrobiopsy was performed that revealed the presence of kidneys AA-amyloidosis. Given these data in conjunction with clinical manifestations, the patient»s nationality, FMF was diagnosed and colchicine 2 mg/day was appointed. It was possible to stop the clinical symptoms of inflammation in FMF, but the nephrotic syndrome due to amyloidosis persists.Conclusion.The presented observation demonstrates the complexity of FMF diagnosis that verified 18 years after the appearance of the first disease symptoms. The diagnosis was helped by the presence of disease clinical manifestations and kidneys morphological study that revealed the development of a serious complication of periodic disease – AA-amyloidosis. Treatment with colchicine allowed to stop the symptoms of periodic disease.

Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

Analysis of a Chlamydia epidemic model with pulse vaccination strategy in a random environment

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate, and pulse vaccination strategy in a random environment. It has been shown that the Chlamydia epidemic model has global positive solutions and, under some conditions, it admits a unique positive periodic disease-free solution, which is globally exponentially stable in mean square. We have defined two positive numbers R1 and R2 (< R1). It is proved that the susceptible population will be persistent in the mean and the disease will be going to extinct if R1 < 1 and the susceptible population as well as the disease will be weakly persistent in the mean if R2 > 1. Our analytical findings are explained through numerical simulation, which show the reliability of our model from the epidemiological point of view.

Correlations between indicators of interleukin-10 and interleukin-6 in patients with periodic disease

Aim. Determination of the concentration of interleukin-10 (IL-10) and interleukin-6 (IL-6) in serum of patients with periodic disease (PD) before and after treatment with colchicin, as well as the identification of correlation between the indicators of these parameters. Materials and methods. We examined 188 patients with PD (89 men, 99 women) aged from 12 to 69 years, as well as 44 patients with rheumatoid arthritis (RA) as a comparison group and 41 healthy people of the control group. Patients were divided into groups: 1 - PD colchicinotherapy patients with seizures without amyloidosis that do not respond to treatment maximum dose of colchicine 2.0 mg/day; 2nd-PD patients without amyloidosis, not responding to treatment 1.5 mg/day colchicine; 3rd - PD patients that responds to certain doses of colchicine (0.5 to 2.0 mg/day); 4th - PD patients without amyloidosis who did not receive treatment; 5-I of the healthy persons of the control group; 6-I - RA patients. The concentration of IL-10 in blood serum was determined by enzyme immunoassay ELISA, and IL-6 - immunochemiluminescent method. For statistical processing the computer program SPSS is used. The results were considered statistically significant at the level of reliability p

Temporal evolution of immunity distributions in a population with waning and boosting

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population, however their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity.We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations, that connects all these processes, and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune-dynamics.AMS Classification92D30, 34K60, 34K34, 37M05