Survival Probability Rates Research Articles

Long-term efficacy, safety, and drug survival of secukinumab in patients with psoriasis in Turkey: a retrospective analysis of real-world experience.

Secukinumab (SEC) has been shown to be highly effective and safe in the treatment of moderate to severe plaque psoriasis (PsO), but data on SEC's long-term drug survival are limited. To analyse the survival rate of SEC and its predictive factors of survival, together with the drug safety and efficacy. Data of 268 patients who received SEC between May 2018 and April 2022 with moderate to severe psoriasis and/or psoriatic arthritis were analysed retrospectively. Psoriasis Area Severity Index (PASI) was used to define effectiveness. Drug survival was examined using the Kaplan-Meier analysis and Cox regression analysis was used to analyse predictive factors. PASI 75/90/100 responses achieved at week 16 (89.5%, 78%, and 16.2%, respectively) were well maintained at week 52 (96.3%, 90.7%, and 15.4%, respectively). The drug survival probability rates for SEC were 94.4% at 12 months, 88.4% at 24 months, 78.6% after 3 years, 52.7% after 4 years. Concomitant treatments, dose escalation and family history of psoriasis were associated with a higher risk for SEC withdrawal. Close monitoring may improve SEC survival in psoriasis patients who require dose escalation and concomitant drugs.

Survival rate of laryngeal cancer patients treated in Brazil's Unified Health System - SUS, 2002-2010

The scope of this article was to analyze the five-year survival rate among patients with laryngeal cancer treated in the Unified Health System in Brazil and its regions between January 2002 and June 2010. There is still scarce information in Brazil regarding the scale and survival rate of laryngeal cancer patients, which makes it difficult to adopt specific strategies for the control of the condition in the country. A retrospective cohort study based on the National Oncology Database was conducted, and the survival probability rate for laryngeal cancer according to age, sex and Brazilian regions/states was estimated using the Kaplan-Meier method. The log-rank test was used to assess the differences observed, considering a 5% significance level. Survival in Brazil was estimated at 50.8% (95%CI: 49.9%-51.8%), being lower among male patients (49.1%; 95%CI: 48.10%-50.16%); between 50 and 60 years of age (48.4%; 95%CI: 46.7%-50.0%); for residents of the Northern region (45.5%; 95%CI: 39.5%-51.3%). The regional variation in the survival rate for laryngeal cancer in Brazil reveals disparities between Brazilian regions/states that may be linked to inequality of access to diagnosis and/or treatment.

Clinical Manifestations.

Impulse dyscontrol, i.e., excessive motor activity and/or physical and verbal aggression is common in dementia. However, impulse dyscontrol can also emerge in advance of dementia, but is often normalized due to age, or framed as a psychiatric condition. Thus, the association between these symptoms and incident dementia is unclear. Mild behavioral impairment (MBI) leverages risk associated with later-life emergent and persistent neuropsychiatric symptoms (NPS) to identify a high-risk group for incident dementia. Impulse dyscontrol is one of five MBI domains. Here, in dementia-free participants, we assessed risk of progression to dementia in MBI-impulse dyscontrol and conventionally-measured impulse dyscontrol symptoms (Conv-ID). Dementia-free National Alzheimer Coordinating Centre participants were included. Neuropsychiatric Inventory Questionnaire irritability, agitation, and aberrant motor behavior items were used to identify impulse dyscontrol. MBI-impulse dyscontrol was operationalized by symptom presence at more than two-thirds of pre-dementia study visits (symptom persistence criterion) in those with no history of psychiatric disorders (symptom emergence criterion). Conv-ID required symptoms only at baseline without consideration of past psychiatric history. Kaplan-Meier survival curves and Cox proportional hazards models, adjusted for age, sex, education, race, and APOE-e4 status, were generated to compare survival probability and dementia incidence rates of MBI-impulse dyscontrol and Conv-ID to No-NPS. The sample comprised 1,884 MBI-impulse dyscontrol (age = 74.5±9.7; 40.9% female), 3,676 Conv-ID (age = 71.0±9.4; 47.0% female), and 6,362 No-NPS participants (age = 71.0±10.3; 64.7% female) (Table 1). MBI-impulse dyscontrol had lower dementia-free survival (p<0.0001) and 2.23-fold greater dementia incidence compared to No-NPS (CI:1.99-2.50, p<0.001, Figure 1(A)); Conv-ID had lower dementia-free survival (p<0.0001) and 1.39-fold greater dementia incidence compared to No-NPS (CI:1.25-1.54, p<0.001, Figure 1(B)). Compared with a conventional approach to assess agitated and impulsive behaviors, MBI-impulse dyscontrol was associated with greater dementia incidence. Applying the MBI criteria of later-life emergence and persistence of symptoms provides a more specific approach to identify those at risk for incident dementia, who might otherwise be dismissed due to normalization of these behaviors in older persons or labelled with a psychiatric condition. This approach may allow for earlier implementation of preventative measures, pharmacological and non-pharmacological, improving outcomes and quality of life for patients and their caregivers.

Early Celecoxib use in Patients with Traumatic Brain Injury.

Traumatic brain injury (TBI) can cause rapid brain inflammation. There is debate over the safety and efficacy of anti-inflammatory agents in its treatment. With a particular focus on cyclooxygenase 2 (COX2) selective inhibition, we sought to determine the impact of celecoxib versus no celecoxib treatment on outcomes in patients with TBI and compare these with outcomes associated with nonselective COX inhibition (ibuprofen) and corticosteroid (dexamethasone) treatment. This retrospective cohort study used TriNetX, a large publicly available global health research network, to gather clinical data extracted from the electronic medical records. Using International Classification of Diseases, Tenth Revision and pharmacy codes, we identified patients with TBI who were and were not treated with celecoxib, ibuprofen, and dexamethasone. Analysis was performed on propensity-matched and unmatched cohorts, which were matched on demographics, comorbidities, and neurological injuries. Our primary end point was 1-year survival. Secondary end points were ventilator and tracheostomy dependence, gastrostomytube placement, seizures, and craniotomy. After propensity score matching, a total of 1443 patients were identified in both the celecoxib and no celecoxib cohorts. Ninety-two (6.4%) patients in the celecoxib cohort died within 1year following TBI versus 145 (10.0%) in the no celecoxib cohort (odds ratio 0.61; 95% confidence interval 0.46-0.80; p = 0.0003). The 1-year survival rate was 96.1% in the celecoxib cohort versus 93.1% in the no celecoxib cohort (p < 0.0001). At the end of the 1-year period, celecoxib was associated with significantly lower gastrostomy tube dependence (p = 0.017), seizure activity (p = 0.027), and myocardial infarction (p = 0.021) compared with the control cohort. Ibuprofen was also associated with higher 1-year survival probability and lower rates of post-TBI complications. Dexamethasone was broadly associated with higher morbidity but was associated with higher 1-year survival probability compared with the no dexamethasone cohort. Early celecoxib and ibuprofen use within 5days post TBI was associated with higher 1-year survival probabilities and fewer complications. With emerging yet controversial preclinical evidence to suggest that COX inhibition improves TBI outcomes, this population-level study offers suggestive support for these drugs' clinical benefit, which should be pursued in prospective clinical studies.

Population dynamics of the last leopard population of eastern Indochina in the context of improved law enforcement

Poaching, a major threat to wildlife worldwide, is pushing species toward extinction. To reduce poaching pressure and combat biodiversity loss, improved law-enforcement efforts reportedly are required; the effectiveness of which can be determined through rigorous monitoring of wildlife populations, particularly of endangered large carnivores. In the Eastern Plains Landscape of Cambodia, law-enforcement efforts increased to counter the severe threats from illegal activities; however, it is unknown if these strategies are benefiting the population of the Critically Endangered Indochinese leopard (Panthera pardus delacouri), the last large felid population of eastern Indochina. We used open population spatial capture-recapture models to estimate density, survival, per-capita recruitment, and population growth rates of leopard using data from 7 camera-trap surveys conducted over 11 years (2009–2019). We found that the population (a) declined by over 82 % (from 1.5 to 0.3 leopard/100 km2), (b) had low survival probability (0.58) and low recruitment rates (males: 0.04, females: 0.24), and (c) is expected to continue declining. An additional survey in 2021 failed to detect leopard, suggesting the species now is functionally extinct, if not fully extirpated, from the landscape. Over the study period, there was a drastic increase in human activity, with a 20-fold increase in detection frequencies of humans and a 1000-fold increase in lethal-trap encounter rate. The rise in anthropogenic pressures, particularly snaring, appeared to be the primary reason for the leopard decline, indicating the last decade of management interventions was insufficient to conserve the species, which now appears to be extirpated in all of Cambodia, Laos and Vietnam. This has implications for leopard conservation in the wider region, notably that efforts should now focus on populations within the two remaining strongholds. Our results suggest that increases in law-enforcement efforts alone are unlikely to protect wildlife in eastern Indochina; thus, additional strategies are needed to address the region's snaring crisis, including legislative reforms, community engagement, and programs that reduce demand for wildlife meat and products. Long-term studies of remaining Indochinese leopard populations coupled with timely and effective conservation actions are needed to avoid the complete demise of this subspecies.

Interventional oncological treatment of breast cancer liver metastasis (BCLM): single center long-term evaluation over 26 years using thermoablation techniques like LITT, MWA and TACE in a multimodal application

The purpose of the study is to retrospectively evaluate the development and technological progress in local oncological treatments of patients with breast cancer liver metastasis (BCLM) using LITT (laser interstitial thermotherapy), MWA (microwave ablation) and TACE (transarterial chemoembolization) ablation techniques in a multimodal application. The study uses data generated between 1993 and 2020. Therapy results were evaluated using the Kaplan–Meier survival estimate, Cox proportional hazard regression and log-rank test. Cox regression analysis showed that the different treatment methods are statistically significant predictors of survival of patients. Median survival times for groups treated with LITT (212 patients) and LITT + TACE (215 patients) were 2.2 years and 2.1 years respectively; median survival times for groups treated with MWA (17 patients) and MWA + TACE (143 patients) were 5.6 and 2.4 years respectively. For LITT only treatments, the 1-, 3- and 5-year survival probability scored 80%, 37%, 22%. Results for combined LITT + TACE treatments were 76%, 34% and 15%. In group MWA, the 1-/3-/5-year survival probability rates were calculated as 89%, 89%, 89% (however, they should be interpreted carefully due to a relatively small sample size of n = 17 patients). Group MWA + TACE offered values of 77%, 38% and 22%. A separate group of 549 patients was analyzed with TACE monotherapy treatment. The estimated median survival time in this group was 0.8 years. The 1-/3-/5-year survival probability rates were 37%, 8% and 4%. Treatments with combined MWA and MWA + TACE resulted in the best median survival time estimations in this study.

PROGNOSTIC VALUE OF LOW-DOSE ADRENOCORTICOTROPIC HORMONE TEST IN CRITICALLY ILL PATIENTS.

Background: Previous trials evaluated the incidence of critical illness-related corticosteroid insufficiency (CIRCI) using 250 μg adrenocorticotropic hormone (ACTH). However, this supraphysiological dose could result in false-positive levels. We aimed to determine the incidence of CIRCI in septic patients using a 1 μg ACTH stress test. Methods: We conducted a prospective cohort study on 39 patients with septic shock. Critical illness-related corticosteroid insufficiency was defined as a Δ max cortisol <9 μg/dL after 1 μg ACTH stress test. The primary outcome of the study was death. Secondary outcomes included days of vasopressors, days of mechanical ventilation (MV), amount of fluid per day, the incidence of acute kidney injury (AKI), and days of intensive care unit (ICU) stay. Results: The incidence of CIRCI in our cohort was 43.6% using 1 μg ACTH. There were no significant differences between groups in terms of ICU scores, laboratory investigations, vasopressors, MV days, amount of fluid per day, and the ICU stay ( P = > 0.05). The CIRCI group had lower median survival and survival probability rates (5 days and 48.4%, respectively) compared with the non-CIRCI group (7 days and 49.5%, respectively). In addition, the CIRCI group had a shorter time to develop AKI and a higher probability of developing AKI (4 days and 44.6%, respectively) in comparison with the non-CIRCI group (6 days and 45.57%, respectively). Conclusion: We concluded that the CIRCI group had a lower mean survival rate and a higher incidence of AKI. We recommend the use of 1 μg ACTH test in septic shock patients to identify this subgroup of patients.

Gaussian mixture probability hypothesis density filter with dynamic probabilities: Application to road traffic surveillance

With the development of autonomous driving system, accurate tracking of the number of vehicles and their states is critical to ensure traffic safety. Since the numbers and states of the vehicles are unknown and time-varying, the road traffic surveillance can be considered as a multiple-target tracking (MTT) problem. The Gaussian mixture probability hypothesis density (GM-PHD) filter is a popular approach in solving MTT problem and has been successfully applied to a range of applications including ground vehicle tracking. However, due to the road constraint, the maneuverability of a ground vehicle is limited to the road lane. Thus, the target detection probability, survival probability, and birth rate, which are assumed to be constant in the original GM-PHD filter, vary according to the surveillance area as well as its own state. To address this, we propose an algorithm that dynamically updates the probability of detection and survival, and birth rate simultaneously in a mathematically rigorous way. This is done by integrating the semantic information inferred from the environment with the state-dependent GM-PHD filter. The performance and effectiveness of the proposed algorithm are demonstrated via illustrative road traffic scenarios.

The cost of recharging infrastructure for electric vehicles in the EU in a climate neutrality context: Factors influencing investments in 2030 and 2050

The electrification of passenger cars is a cornerstone of the EU strategy to decarbonising European transport by 2050. A key step for the uptake of electric vehicles (EVs) is to scale up the rollout of rechargers. The paper assesses which factors influence the investments in EU recharging infrastructure in a context of ambitious EV deployment projected under the “Fitfor55” policy package of the European Commission. We use an energy-demand method that includes assumptions on charging requirements of different EV types, the structure of the charging fleet, the survival probability and learning rates of the rechargers and conduct a sensitivity analysis to quantify their impact on investments. The projected electricity share in passenger cars is about 4.5% (65 TWh) and the required infrastructure ranges between 3.2 and 4million chargers in 2030, while investments range between 8.7 and 16.2bn€ in 2021–2030. By mid-century, the electrification share of passenger cars increases to 62% (285 TWh) for which we estimate a total demand of 13.6 to 20.3million chargers and an additional 44.3 to 80.3bn€ of investments in 2031–2050. A regression analysis depicts a strong correlation between fast chargers and investment expenditures, which is particularly relevant for 2021–2030, a period, when the deployment of a fast charging network will be needed to help reduce charging times and enable the roll-out of EVs. The energy output per charging point is the second most influential factor. Other factors, while important, are found not to significantly affect system costs.

Importance of local weather and environmental gradients on demography of a broadly distributed temperate frog

Amphibian populations are sensitive to environmental temperatures and moisture, which vary with local weather conditions and may reach new norms and extremes as contemporary climate change progresses. Using long-term (11–16 years) mark-recapture data from 10 populations of the Columbia spotted frog (Rana luteiventris) from across its U.S. range, we addressed hypotheses about how demographic relationships to weather depend upon a population’s position along climate gradients. We estimated the effect of seasonal weather on annual survival probability and recruitment rates both within populations and across the species’ range from subalpine forests to semi-arid deserts. We calculated population-specific weather variables that captured seasonal temperature and precipitation between summer sampling events, both for periods when frogs were active (spring to fall) and inactive (winter). Across all populations, we marked 15,885 adult frogs, with 33% of frogs recaptured at least once. Population demography varied with seasonal weather across the species’ range. Annual adult survival probability and recruitment rates of each population were influenced by a unique set of seasonal temperature and precipitation variables, particularly in winter and spring. Hence, adult survival varied with local conditions but, when analyzed across all populations, was predictable along a species-environment response curve associated with the timing of snowmelt and spring moisture. In contrast, recruitment rates for each population peaked at different values along an environmental gradient associated with the amount of snow during winter, and fall temperature and moisture levels, suggesting that recruitment may be responding to local conditions independently within each population. These findings highlight that sampling across the environmental (i.e., elevational and meteorological) gradients within a species range is necessary to predict species-level responses to regional climate change. This study also provides evidence of the importance of winter conditions on the demography of temperate amphibians, conditions that are already responding to climate change. Finally, this study further emphasizes that local context and spatiotemporal scale of inquiry remain paramount to understanding and potentially managing for climate effects on populations of amphibian species with broad geographic ranges.

Assessing the Role of Venetoclax in Combination with Hypomethylating Agents in Higher Risk Myelodysplastic Syndromes

Assessing the Role of Venetoclax in Combination with Hypomethylating Agents in Higher Risk Myelodysplastic Syndromes

Long-term outcome of tyrosine kinase inhibitor treatment in children and adolescents with newly diagnosed chronic myeloid leukemia in chronic phase.

Long-term outcome of tyrosine kinase inhibitor treatment in children and adolescents with newly diagnosed chronic myeloid leukemia in chronic phase.

Expression and prognostic value of CDK1, CCNA2, and CCNB1 gene clusters in human breast cancer.

ObjectiveCell cycle-associated proteins play important roles in breast cancer (BRCA), based on evidence from cell lines, preclinical murine models, and human tissue samples.MethodsHerein, we used the Onomine, GEPIA, Kaplan–Meier Plotter, and cBioPortal databases to examine transcriptional and survival data pertaining to cyclin-associated gene clusters (CDK1, CCNA2, and CCNB1) in BRCA patients.ResultsCDK1, CCNA2, and CCNB1 gene expression levels were higher in BRCA compared with control tissue samples and were correlated with more-advanced tumor stage. Kaplan–Meier survival analyses confirmed that elevated CDK1, CCNA2, and CCNB1 expression levels were associated with overall and post-progression survival and recurrence-free probability rates in patients with BRCA.ConclusionThe results of this study implied that CDK1, CCNA2, and CCNB1 gene clusters may provide potential therapeutic targets and prognostic biomarkers in patients with BRCA.

Factors affecting survival of seedling of Afzelia africana, a threatened tropical timber species in West Africa

Understanding abiotic and biotic factors affecting the survival of seedlings of threatened species such as Afzelia africana is fundamental for restoration and sustainable management purposes. This study used seedling individual-level morphological data and plot-level data to assess the effect of abiotic (season, elevation, soil type and terrain slope) and biotic (seedling initial density, basal diameter, height and number of leaves, insect and fungal infection, insect herbivory, mammal herbivory, vegetation type, adult conspecific density and diameter, and heterospecific density and diameter) factors on the survival probability (at individual level) and survival rate (at plot level) of seedlings of A. africana in the Pendjari Biosphere Reserve. Generalized Linear Mixed Models (GLMMs) were used for data analyses. At individual level, we found that the survival probability of A. africana seedlings increased with initial height, but decreased from wet to dry season. At plot level, the survival rate of A. africana seedlings also decreased from the wet season (0.72 ± 0.05) to the dry season (0.18 ± 0.04) and was inversely proportional to seedling basal diameter (P = 0.024) and density of conspecific adults (P = 0.016). There were also positive effects of seedling initial height (P = 0.026) and mean diameter of conspecific adults (P = 0.037) on survival rate. Among abiotic factors, only terrain slope showed significant and negative effect (P = 0.028) on the survival rate, suggesting higher survival rate on flat terrain. Our findings suggest that sustainably managing seedlings of A. africana would require accounting for conspecific neighboring effect, terrain slope and season-specific actions. Practical aspects of these factors were further discussed.

Fatigue reliability evaluation of Q460 welded joints using fracture fatigue entropy method

In this paper, the fracture fatigue entropy (FFE) was used to evaluate the fatigue reliability of Q460 welded joints during high-cycle fatigue. The Q460 butt welded joint fatigue tests were conducted under different loads. Meanwhile, the real-time temperature measurement, monitored by an infrared thermal scanner, was completed. The fatigue limit can be well estimated according to the cumulative damage entropy production rate in Phase II, and compared with the fatigue limit prediction value by the traditional staircase method, a good consistency is achieved. Furthermore, the P-S-N curves of 5%, 50%, and 95% survival probability rate are well predicted, which is consistent with the experimental data. Therefore, based on this, the accurate fatigue reliability evaluation based on the proposed method has been achieved.

Investigation of the Self-Heating of Q460 Butt Joints and an S-N Curve Modeling Method Based on Infrared Thermographic Data for High-Cycle Fatigue

In this study, we investigated the fatigue behavior of Q460 welded joints using tensile fatigue tests. Furthermore, real-time temperature profiles of the examined specimens were recorded by infrared thermography. Based on the obtained thermographic data, we calculated the entropy production rate of the specimens under different stress amplitudes. Hypothetically, the entropy production during high-cycle fatigue (HCF) could be divided into two parts. The first is induced by inelastic behavior that corresponds to damage accumulation, and the second originates from anelasticity associated with recoverable non-damaging microstructural motions. The turning point of entropy production under different stress levels represents an index for fatigue limit estimation. Then, considering the average damage threshold that exists during HCF, the entropy production related to damage accumulation (cumulative damage entropy) is obtained by testing three specimens under the same stress amplitude above the fatigue limit. Finally, a rapid three-parameter S-N curve with a survival probability rate of 50% is obtained. Then, combined with the maximum likelihood method, the 5% and 95% survival probability rate S-N curves are established. Most of experimental data are distributed in the area between S-N curves that correspond to 5% and 95% survival probability rate, indicating good accordance with the test data.

Polymer-assisted intratumoral delivery of ethanol: Preclinical investigation of safety and efficacy in a murine breast cancer model.

Focal tumor ablation with ethanol could provide benefits in low-resource settings because of its low overall cost, minimal imaging technology requirements, and acceptable clinical outcomes. Unfortunately, ethanol ablation is not commonly utilized because of a lack of predictability of the ablation zone, caused by inefficient retention of ethanol at the injection site. To create a predictable zone of ablation, we have developed a polymer-assisted ablation method using ethyl cellulose (EC) mixed with ethanol. EC is ethanol-soluble and water-insoluble, allowing for EC-ethanol to be injected as a liquid and precipitate into a solid, occluding the leakage of ethanol upon contact with tissue. The aims of this study were to compare the 1) safety, 2) release kinetics, 3) spatial distribution, 4) necrotic volume, and 5) overall survival of EC-ethanol to conventional ethanol ablation in a murine breast tumor model. Non-target tissue damage was monitored through localized adverse events recording, ethanol release kinetics with Raman spectroscopy, injectate distribution with in vivo imaging, target-tissue necrosis with NADH-diaphorase staining, and overall survival by proxy of tumor growth. EC-ethanol exhibited decreased localized adverse events, a slowing of the release rate of ethanol, more compact injection zones, 5-fold increase in target-tissue necrosis, and longer overall survival rates compared to the same volume of pure ethanol. A single 150 μL dose of 6% EC-ethanol achieved a similar survival probability rates to six daily 50 μL doses of pure ethanol used to simulate a slow-release of ethanol over 6 days. Taken together, these results demonstrate that EC-ethanol is safer and more effective than ethanol alone for ablating tumors.

The search for hypercompetition: evidence from a Nordic market study

ABSTRACT Some scholars and practitioners argue that markets have become hypercompetitive, decreasing the opportunities for sustainable competitive advantage. We test for increasing competition in a panel of 266 Danish firms from 7 industries over the period 1980–2017. We find no support for the argument that the market across industries has become hypercompetitive over this period. The durability of abnormal business returns has remained stable. Dynamism only changed in the 1980s, and levels of munificence are also stable. We do, however, find a small decrease in the survival probability rate of firms over time. Our results lead us to caution against the use of hypercompetition as a universal label for the state of contemporary competition.

A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters

Temperature is one of the integral environmental drivers that strongly affect the distribution and density of tsetse fly population. Precisely, ectotherm performance measures, such as development rate, survival probability and reproductive rate, increase from low values (even zero) at critical minimum temperature, peak at an optimum temperature and then decline to low levels (even zero) at a critical maximum temperature. In this study, a fractional-order Trypanosoma brucei rhodesiense model incorporating vector saturation and temperature dependent parameters is considered. The proposed model incorporates the interplay between vectors and two hosts, humans and animals. We computed the basic reproduction number and established results on the threshold dynamics. Meanwhile, we explored the effects of vector control and screening of infected host on long-term disease dynamics. We determine threshold levels essential to reducing the basic reproduction number to level below unity at various temperature levels. Our findings indicate that vector control and host screening could significantly control spread of the disease at different temperature levels.

Reaction-diffusion approach to electronic relaxation in solution: Simple derivation for delta function sink models

We propose a very simple method for finding the exact analytical solution for the problem of electronic relaxation in solution, modelled by a particle undergoing diffusive motion under any arbitrary potential in presence of a Dirac delta function sink. The diffusive motion of the molecule is modeled by Smoluchowski equation in one dimension. The exact analytical expression of survival probability and different rate constants have been derived for different potentials. The knowledge of Green’s function in Laplace domain without the sink is required for using our method. Our method is very simple in comparison to the earlier method.