A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19.

The spatial movement of the human population from one region to another and the existence of super-spreaders are the main factors that enhanced the disease incidence. Super-spreaders refer to the individuals having transmitting ability to multiple pathogens. In this article, an epidemic model with spatial and temporal effects is formulated to analyze the impact of some preventing measures of COVID-19. The model is developed using six nonlinear partial differential equations. The infectious individuals are sub-divided into symptomatic, asymptomatic and super-spreader classes. In this study, we focused on the rigorous qualitative analysis of the reaction-diffusion model. The fundamental mathematical properties of the proposed COVID-19 epidemic model such as boundedness, positivity, and invariant region of the problem solution are derived, which ensure the validity of the proposed model. The model equilibria and its stability analysis for both local and global cases have been presented. The normalized sensitivity analysis of the model is carried out in order to observe the crucial factors in the transmission of infection. Furthermore, an efficient numerical scheme is applied to solve the proposed model and detailed simulation are performed. Based on the graphical observation, diffusion in the context of confined public gatherings is observed to significantly inhibit the spread of infection when compared to the absence of diffusion. This is especially important in scenarios where super-spreaders may play a major role in transmission. The impact of some non-pharmaceutical interventions are illustrated graphically with and without diffusion. We believe that the present investigation will be beneficial in understanding the complex dynamics and control of COVID-19 under various non-pharmaceutical interventions.

A numerical study of spatio-temporal COVID-19 vaccine model via finite-difference operator-splitting and meshless techniques.

In this paper, a new spatio-temporal model is formulated to study the spread of coronavirus infection (COVID-19) in a spatially heterogeneous environment with the impact of vaccination. Initially, a detailed qualitative analysis of the spatio-temporal model is presented. The existence, uniqueness, positivity, and boundedness of the model solution are investigated. Local asymptotical stability of the diffusive COVID-19 model at steady state is carried out using well-known criteria. Moreover, a suitable nonlinear Lyapunov functional is constructed for the global asymptotical stability of the spatio-temporal model. Further, the model is solved numerically based on uniform and non-uniform initial conditions. Two different numerical schemes named: finite difference operator-splitting and mesh-free operator-splitting based on multi-quadratic radial basis functions are implemented in the numerical study. The impact of diffusion as well as some pharmaceutical and non-pharmaceutical control measures, i.e., reducing an effective contact causing infection transmission, vaccination rate and vaccine waning rate on the disease dynamics is presented in a spatially heterogeneous environment. Furthermore, the impact of the  aforementioned interventions is investigated with and without diffusion on the incidence of disease. The simulation results conclude that the random motion of individuals has a significant impact on the disease dynamics and helps in setting a better control strategy for disease eradication.

Numerical solution of COVID-19 pandemic model via finite difference and meshless techniques.

In the present paper, a reaction-diffusion epidemic mathematical model is proposed for analysis of the transmission mechanism of the novel coronavirus disease 2019 (COVID-19). The mathematical model contains six-time and space-dependent classes, namely; Susceptible, Exposed, Asymptomatically infected, Symptomatic infected, Quarantine, and Recovered or Removed (SEQIaIsR). The threshold number R0 is calculated by utilizing the next-generation matrix approach. In addition to the simple explicit procedure, the mathematical epidemiological model with diffusion is simulated through the operator splitting approach based on finite difference and meshless methods. Stability analysis of the disease free and endemic equilibrium points of the model is investigated. Simulation results of the model with and without diffusion are presented in detail. A comparison of the obtained numerical results of both the models is performed in the absence of an exact solution. The correctness of the solution is verified through mutual comparison and partly, via theoretical analysis as well.

Impacts of severity of Covid-19 infection on the morbidity and mortality of surgical patients.

Introduction: One of the challenges of surgery on patients with active SARS-CoV-2(severe acute respiratory syndrome coronavirus 2) infection is the increased risk of postoperative morbidity and mortality. Aim: This study will describe and compare the postoperative morbidity and mortality in asymptomatic patients or those with mild infection with those with severe COVID-19 infection undergoing elective or and emergency surgery. Materials and methods: This is a retrospective study of 37 COVID19 patients who had the infection 7 days prior to and 30 days after emergency or elective surgery. Patients were divided to two groups. Group1: the asymptomatic or those with mild infection that is diagnosed just before surgery (14 patients). Group 2: those who were admitted to the hospital because of severe COVID-19 and were operated for COVID-19 related complications (23 patients). Morbidity and mortality of both groups was studied. Results: There was no significant difference in gender between the two groups. There were 5 females (2 in group 1, and 3 in group 2) and 32 males (12 in group 1, and 20 in group 2). Mean age for all patients was 49.8years (38 for group 1 and 57 for group2). Median age for all patients was 50 years (37.5 for group 1 and 57 years for group 2). Sepsis developed in 7 patients (1 patient in group 1 and in 6 patients in group 2). Statistically there was no significant difference in occurrence of sepsis between the two groups. There was a significant difference in the intensive care stay between the two groups (higher in group 2). Four deaths were reported in group 1 and fourteen in group 2. Eighteen out of thirty-seven patients died. Conclusion: Severity of COVID-19 infection will prolong the hospitalization and ICU stay in surgical patients with no significant effect on mortality.

Tailgut cysts in children: a report of two cases and literature review.

Tailgut cysts are rare congenital lesions that typically manifest as a presacral, retrorectal, multicystic mass. Even though they are derived from remnants of the embryonic tailgut, they most often present in women. Differential diagnosis includes rectal duplication cyst, sacrococcygeal teratoma, and anterior meningocele. Treatment demands complete excision to prevent infection and malignant degeneration. Fewer than 20 pediatric cases have been reported. Two further affected children are described, one of whom presented uniquely with urinary tract obstruction and acute renal failure.

Efficacy of bladder irrigation and surveillance program in prevention of urinary tract infections and bladder calculi in children with an ileocystoplasty and bladder neck repair.

PURPOSE: In children with bladder augmentation and particularly in those with bladder neck repair (BNR), urinary tract infections (UTI) and bladder calculi are a recognised problem. Bladder irrigation potentially prevents these complications. Our aim was to investigate the efficacy of bladder irrigation supported by a surveillance program in prevention of UTI and bladder calculi in these children. METHODS: A cohort of children subjected to ileocystoplasty with a stoma for clean intermittent self catheterisation with or without BNR was retrospectively analysed. The children were subjected to bladder irrigation and monitored by Clinical Nurse Specialists (CNS) according to a protocol. Patients' demographics, treatment methods and postoperative management were reviewed. Compliance to bladder irrigation was assessed with questionnaires. UTI recurrence and bladder calculi during follow-up were assessed. RESULTS: 28 children were included in this study. The median follow-up was 48 months (range 6-87). Compliance could be assessed in all children, except in one child (3.5%). There was no recurrent UTI reported, bladder calculi occurred in two children (7%). CONCLUSION: Our bladder irrigation regime resulted in a low incidence of calculi by preventing recurrent UTI. The surveillance program resulted in high compliance rates in children with an augmented bladder with or without BNR.

Mesoblastic nephroma: a report of the United Kingdom Children's Cancer and Leukaemia Group (CCLG).

BACKGROUND: Mesoblastic nephroma (MN) is a rare tumour which occurs mainly in early infancy and for which primary nephrectomy is the treatment of choice. This study aimed to assess surgical complications and outcomes in this patient group and to re-evaluate the age threshold of 6 months for recommending primary nephrectomy. PROCEDURE: A retrospective file review of all cases of MN registered in UK Children's Cancer and Leukaemia Group renal tumour trials between October 1991 and March 2008. Data from the trials were compared with data held by the National Registry of Childhood Tumours, Oxford. RESULTS: Forty-seven (3.5%) confirmed cases of MN were found among 1346 registered renal tumours. Median age at diagnosis was 30 days (range birth-3.8 years). MN was significantly more common in the first 3 months of life compared to between 3 and 6 months (33 vs. 2 cases). Seven cases occurred between 6 months and 1 year and only five cases occurred beyond 1 year of age. There was a significant difference in the age of diagnosis by histological subtype. There were 11 complications in the series; no registered patient developed a recurrent tumour; and all were alive at last follow-up. CONCLUSIONS: Outcome for children with MN is excellent at all ages, with little indication for adjuvant chemotherapy. Children presenting at <3 months of age, should be treated by primary nephrectomy. In those presenting aged >3 months, alternative diagnoses should be considered, especially in the presence of surgical risk factors.

Endoscopic insertion of cystostomy button for bladder drainage in children.

AIM: The aim of this study is to describe a safe and simple minimally invasive technique for insertion of cystostomy buttons for bladder drainage and cycling in children. MATERIAL AND METHODS: This is part of an ongoing prospective study since 2002 looking at our experience with insertion of cystostomy buttons in children. We recently published the results of the use of cystostomy buttons in 17 children inserted by an open technique reporting minor complications of urinary leakage and wound infection. We have modified our practice in the last 2 years to a percutaneous endoscopic approach. RESULTS: Twelve children (four girls, eight boys) with a mean age of 7.1 years underwent endoscopic insertion of a cystostomy button. Mean follow up was 11 months (3-24 months). There were no complications such as leakage in the endoscopically inserted buttons. CONCLUSIONS: Button cystostomy is a safe and effective form of bladder drainage and gives children a less restricted quality of life. Endoscopic technique allows insertion of buttons under vision with good snug fit and no leakage.

The long-term outcome of prenatally detected posterior urethral valves: a 10 to 23-year follow-up study.

OBJECTIVE: To document the functional outcome of patients with prenatally detected posterior urethral valves (PUV) in the second decade of life, and to evaluate the possible impact of prenatal diagnosis on the long-term outcome of this condition. PATIENTS AND METHODS: We analysed the functional outcome of 25 patients with prenatally detected PUV born between 1984 and 1996, whose mean (range) age at follow-up was 17.7 (10-23) years. The findings were compared with those in 17 patients (mean age 16.1 years) who had presented clinically to our unit during the same period. The duration of follow-up in both groups was >or=10 years. Late outcomes were also compared with published data for PUV. Outcome measures included; death, incidence of end-stage renal failure (ESRF), age at transplantation and the most the recently available plasma creatinine level in untransplanted patients. We also examined any possible association between functional outcome and early predictors, including nadir plasma creatinine level at <1 year and vesico-ureteric reflux (VUR). RESULTS: Three patients died (12%), two as neonates and one aged 3 years. Of five patients who had been shunted in utero, four died or developed early-onset renal failure. In the 23 prenatally detected patients who survived the neonatal period, four (17%) had a renal transplant at a mean (range) age of 6.5 (3.0-12.0) years. Of 19 patients with prenatally detected PUV who had not been transplanted in the first 12 years of life, only one (5%) developed new-onset ESRF at 10.0-23.4 years whilst 11 (58%) of these patients had normal creatinine values. In the untransplanted patients there was a statistically significant correlation between age and plasma creatinine level, but no correlation between late functional outcome and nadir creatinine in the first year of life, or bilateral VUR. CONCLUSIONS: Prenatal diagnosis had little impact on mortality or ESRF in the first decade of life. This appears to be largely predetermined by renal dysplasia and the severity of intrauterine obstruction. However, the functional outcome of patients with prenatally detected PUV aged 10-23 years was considerably better than published long-term data and the outcome of clinically presenting patients in our study. These findings suggest that the long-term prognosis of PUV of intermediate severity might be improved by prenatal diagnosis.

Ultrasound diagnosis of infantile hypertrophic pyloric stenosis: determinants of pyloric length and the effect of prematurity.

AIM: To evaluate the determinants of sonographic measurements of pyloric length and muscle thickness in infants with hypertrophic pyloric stenosis (HPS) and to determine whether infants born prematurely have proportionately smaller measurements. MATERIALS AND METHODS: A retrospective review was carried out of 190 infants operated on for HPS at Bristol Children's Hospital over a 5-year period. Sonographic measurements of pyloric length and muscle thickness were related to age, history of prematurity, weight, sex and family history of HPS. RESULTS: Pyloric length in infants with HPS was significantly greater in those born at term compared to those born prematurely (18.6 mm [SD 2.2] vs 17.3 mm [SD 3.1], P = 0.043); this was explainable by body weight, with length increasing by 1.13 mm (SE 0.35) per kilogram (P = 0.002). There was no significant relationship with measured muscle thickness. CONCLUSION: Sonographic measurement of pyloric length is strongly correlated with the weight of the infant, irrespective of other factors. The relationship of length and weight may be useful in confirming the presence of HPS in small and premature infants.