Figure 1.
Manuscript statistics from 2020 to 2022.
This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater Ⅲ and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater Ⅲ and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics.
Citation: Mostafa M. A. Khater, Mohammed Zakarya, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty. Dynamics and stability analysis of nonlinear DNA molecules: Insights from the Peyrard-Bishop model[J]. AIMS Mathematics, 2024, 9(9): 23449-23467. doi: 10.3934/math.20241140
| [1] | Kelly Pagidas . 2024 Annual Report. AIMS Medical Science, 2025, 12(1): 63-68. doi: 10.3934/medsci.2025005 |
| [2] | Ragini C Bhake, Stafford L Lightman . A Simple Complex Case: Restoration of Circadian Cortisol Activity. AIMS Medical Science, 2015, 2(3): 182-185. doi: 10.3934/medsci.2015.3.182 |
| [3] | Mpumelelo Nyathi, Autherlia Dimpho Rinkie Mosiame . Evaluating radiation exposure risks from patient urine in a PET-CT center: should concerns arise?. AIMS Medical Science, 2025, 12(2): 238-246. doi: 10.3934/medsci.2025016 |
| [4] | Piero Pavone, Ottavia Avola, Claudia Oliva, Alessandra Di Nora, Tiziana Timpanaro, Chiara Nannola, Filippo Greco, Raffaele Falsaperla, Agata Polizzi . Genetic epilepsy and role of mutation variants in 27 epileptic children: results from a “single tertiary centre” and literature review. AIMS Medical Science, 2024, 11(3): 330-347. doi: 10.3934/medsci.2024023 |
| [5] | Muhammad Bilal . Leukemoid reaction in paraplegic male with pressure injuries: A case report. AIMS Medical Science, 2024, 11(2): 72-76. doi: 10.3934/medsci.2024006 |
| [6] | Niccolò Stomeo, Giacomo Simeone, Leonardo Ciavarella, Giulia Lionetti, Arosh S. Perera Molligoda Arachchige, Francesco Cama . Fluid overload during operative hysteroscopy for metroplasty: A case report. AIMS Medical Science, 2023, 10(4): 310-317. doi: 10.3934/medsci.2023024 |
| [7] | Ryan T. Borne, Arash Aghel, Amit C. Patel, Robert K. Rogers . Innominate Steal Syndrome: A Two Patient Case Report and Review. AIMS Medical Science, 2015, 2(4): 360-370. doi: 10.3934/medsci.2015.4.360 |
| [8] | Rosario Megna . Evolution of the COVID-19 pandemic in Italy at the national and regional levels from February 2020 to March 2022. AIMS Medical Science, 2023, 10(3): 237-258. doi: 10.3934/medsci.2023019 |
| [9] | Juliet A Harvey, Sebastien FM Chastin, Dawn A Skelton . What happened to my legs when I broke my arm?. AIMS Medical Science, 2018, 5(3): 252-258. doi: 10.3934/medsci.2018.3.252 |
| [10] | Jamie L. Flexon, Lisa Stolzenberg, Stewart J. D'Alessio . The effect of cannabis legislation on opioid and benzodiazepine use among aging Americans. AIMS Medical Science, 2024, 11(4): 361-377. doi: 10.3934/medsci.2024025 |
This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater Ⅲ and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater Ⅲ and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics.
It is with admiration that we share with you our publication data for the 2022 calendar year for the AIMS Medical Science Journal. It was another successful year with the highest number of publication submissions to date over the past three years. Our depth and breadth of publications spanned multiple basic and clinical science disciplines that originated from talented authors across the globe. We look forward to an exciting year ahead and welcome the opportunity to review original manuscripts for consideration for publication in the journal. Our goals are to provide a forum of high-quality manuscripts that can positively impact the expansion of scientific knowledge and advance the health of our population.
Below is a graphic depiction of the manuscript submission and publication data for the journal for the past three years (Figure 1). There are slightly more submissions that were received in 2022 than in 2021, and the number of accepted and published manuscripts remain stable for the past three years. Our hope is increasing the footprint of quality manuscripts submitted to the journal that will translate into an increased number of high-quality publications for the upcoming year.
2022 manuscripts status:
Publications: 28
Reject rate: 71%
Publication time (from submission to online): 109 days
The geographic distribution of the corresponding authors of the published manuscripts are depicted below (Figure 2). We are honored to attract authors from around the world who chose to submit their research to the journal for publication (USA, Canada, Nigeria, Japan, etc.). Of note the majority of publications originate from authors based in the United States representing 39% of the publications followed by Canada and Nigeria standing at 11% each.
Table 1 depicts the type of manuscripts published. A total of 28 articles were published in 2022, of which, the majority were research based, 12 (43%) followed by reviews, 10 (36%).
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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Table 2 depicts the top 10 articles with the highest views, published in 2022. A focus of these top 10 articles was: Fall Risks, Monoclonal Antibody development and COVID-19.
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
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AIMS Medical Science Journal has 94 members, representing 26 countries. Thirty three percent of the members are from the United States, and other members represent Italy, France, and several other countries (Figure 3). We want to particularly acknowledge our editors: Kelly Pagidas (Editor-in-Chief), Belgüzar Kara, Gulshan Sunavala-Dossabhoy, Gwendolyn Quinn, Panayota Mitrou, Kimberly Udlis (retired), Mai Alzamel, Yi-Jang Lee, Sreekumar Othumpangat, Ji Hyun Kim, Athanasios Alexiou, Robert Striker, Andrei Kelarev, Casey Peiris, Patrick Legembre, Ramin Ataee, Louis Ragolia, Bogdan Borz, Robert Kratzke, Maria Fiorillo, Lars Malmström, Giuliana Banche, Jean-Marie Exbrayat and Elias El-Habr. Importantly, a special thank you to all the Editorial Board members, reviewers and in-house editors, and staff for their dedication, commitment, and unrelenting hard work throughout the year. We hope to attract additional scholars that will be able to join our team for the upcoming year.
| [1] |
J. Manafian, O. A. Ilhan, S. A. Mohammed, Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model, Aims Mathematics, 5 (2020), 2461–2483. http://doi.org/10.3934/math.2020163 doi: 10.3934/math.2020163
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| [2] |
L. Ouahid, Plenty of soliton solutions to the DNA Peyrard-Bishop equation via two distinctive strategies, Phys. Scr., 96 (2021), 035224. https://doi.org/10.1088/1402-4896/abdc57 doi: 10.1088/1402-4896/abdc57
|
| [3] |
M. B. Riaz, M. Fayyaz, Rahman, R. U., Martinovic, J., O. Tunç, Analytical study of fractional DNA dynamics in the Peyrard-Bishop oscillator-chain model, Ain Shams Eng. J., 15 (2024), 102864. https://doi.org/10.1016/j.asej.2024.102864 doi: 10.1016/j.asej.2024.102864
|
| [4] | K. K. Ali, M. I. Abdelrahman, K. R. Raslan, W. Adel, On analytical and numerical study for the peyrard-bishop DNA dynamic model, Appl. Math. Inf. Sci, 16 (2022), 749–759. |
| [5] |
M. I. Asjad, W. A. Faridi, S. E. Alhazmi, A. Hussanan, The modulation instability analysis and generalized fractional propagating patterns of the Peyrard-Bishop DNA dynamical equation, Opt. Quant. Electron., 55 (2023), 232. https://doi.org/10.1007/s11082-022-04477-y doi: 10.1007/s11082-022-04477-y
|
| [6] |
A. Hussain, M. Usman, F. D. Zaman, S. M. Eldin, Optical solitons with DNA dynamics arising in oscillator-chain of Peyrard-Bishop model, Results Phys., 50 (2023), 106586. https://doi.org/10.1016/j.rinp.2023.106586 doi: 10.1016/j.rinp.2023.106586
|
| [7] |
T. E. Sutantyo, A. Ripai, Z.Abdullah, W. Hidayat, Nonlinear dynamics of modified peyrard-bishop DNA model in nosé-hoover thermostat, J. Phys.: Conf. Ser., 1876 (2021), 012021. https://doi.org/10.1088/1742-6596/1876/1/012021 doi: 10.1088/1742-6596/1876/1/012021
|
| [8] |
M. V. Bezhenar, A. A. Elkina, J. H. Caceres, M. G. Baryshev, A. O. Sulima, S. S. Dzhimak, et al., Review of Mathematical Models Describing the Mechanical Motion in a DNA Molecule, Biophysics, 67 (2022), 867–875. https://doi.org/10.1134/S0006350922060021 doi: 10.1134/S0006350922060021
|
| [9] |
A. Tripathy, S. Sahoo, New dynamic multiwave solutions of the fractional Peyrard-Bishop DNA model, J. Comput. Nonlinear Dyn., 18 (2023), 101005. https://doi.org/10.1115/1.4063223 doi: 10.1115/1.4063223
|
| [10] |
T. E. P. Sutantyo, A. Ripai, Z. Abdullah, W. Hidayat, F. P. Zen, Soliton-like solution on the dynamics of modified Peyrard-Bishop DNA model in the thermostat as a bio-fluid, Emerg. Sci. J., 6 (2022), 667–678. https://doi.org/10.28991/ESJ-2022-06-04-01 doi: 10.28991/ESJ-2022-06-04-01
|
| [11] |
A. Zafar, K. K. Ali, M. Raheel, N. Jafar, K. S. Nisar, Soliton solutions to the DNA Peyrard-Bishop equation with beta-derivative via three distinctive approaches, Eur. Phys. J. Plus, 135 (2020), 726. https://doi.org/10.1140/epjp/s13360-020-00751-8 doi: 10.1140/epjp/s13360-020-00751-8
|
| [12] |
G. Akram, S. Arshed, Z. Imran, Soliton solutions for fractional DNA Peyrard-Bishop equation via the extended-expansion method, Phys. Scr., 96 (2021), 094009. https://doi.org/10.1088/1402-4896/ac0955 doi: 10.1088/1402-4896/ac0955
|
| [13] |
L. Ouahid, M. A. Abdou, S. Owyed, S. Kumar, New optical soliton solutions via two distinctive schemes for the DNA Peyrard-Bishop equation in fractal order, Modern Phys. Lett. B, 35 (2021), 2150444. https://doi.org/10.1142/S0217984921504443 doi: 10.1142/S0217984921504443
|
| [14] |
A. Djine, G. R. Deffo, S. B. Yamgoué, Bifurcation of backward and forward solitary waves in helicoidal Peyrard-Bishop-Dauxois model of DNA, Chaos, Soliton. Fract., 170 (2023), 113334. https://doi.org/10.1016/j.chaos.2023.113334 doi: 10.1016/j.chaos.2023.113334
|
| [15] |
A. Djine, N. O. Nfor, G. R. Deffo, S. B. Yamgoué, Higher order investigation on modulated waves in the Peyrard-Bishop-Dauxois DNA model, Chaos, Soliton. Fract., 181 (2024), 114706. https://doi.org/10.1016/j.chaos.2024.114706 doi: 10.1016/j.chaos.2024.114706
|
| [16] |
R. A. Attia, D. Baleanu, D. Lu, M. Khater, E. S. Ahmed, Computational and numerical simulations for the deoxyribonucleic acid (DNA) model, Discrete Contin. Dyn. Syst.-Ser. S, 14 (2021), 3459–3478. https://doi.org/10.3934/dcdss.2021018 doi: 10.3934/dcdss.2021018
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| [17] |
M. M. Khater, D. Lu, M. Inc, Diverse novel solutions for the ionic current using the microtubule equation based on two recent computational schemes, J. Comput. Electron., 20 (2021), 2604–2613. https://doi.org/10.1007/s10825-021-01810-8 doi: 10.1007/s10825-021-01810-8
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| [18] |
M. M. Khater, A. Jhangeer, H. Rezazadeh, L. Akinyemi, M. A. Akbar, M.Inc, et al., New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques, Opt. Quant. Electron., 53 (2021), 609. https://doi.org/10.1007/s11082-021-03267-2 doi: 10.1007/s11082-021-03267-2
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| [19] | M. M. Khater, S. H. Alfalqi, J. F. Alzaidi, R. A. Attia, Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium, Results Phys., 46 (2023), 106312. |
| [20] |
A. Rani, M. Ashraf, M. Shakeel, Q. Mahmood-Ul-Hassan, J. Ahmad, Analysis of some new wave solutions of DNA-Peyrard-Bishop equation via mathematical method, Modern Phys. Lett. B, 36 (2022), 2250047. https://doi.org/10.1142/S0217984922500476 doi: 10.1142/S0217984922500476
|
| [21] | T. Shafique, M. Abbas, A. Mahmood, F. A. Abdullah, A. S. Alzaidi, T. Nazir, Solitary wave solutions of the fractional Peyrard Bishop DNA model, Opt. Quant. Electron., 56 (2024), 815. |
| [22] |
A. Secer, M. Ozisik, M. Bayram, N. Ozdemir, M. Cinar, Investigation of soliton solutions to the Peyrard-Bishop-Deoxyribo-Nucleic-Acid dynamic model with beta-derivative, Modern Phys. Lett. B, 38 (2024), 2450263. https://doi.org/10.1142/S0217984924502634 doi: 10.1142/S0217984924502634
|
| [23] |
N. A. Jolfaei, N. A. Jolfaei, M. Hekmatifar, A. Piranfar, D. Toghraie, R. Sabetvand, et al., Investigation of thermal properties of DNA structure with precise atomic arrangement via equilibrium and non-equilibrium molecular dynamics approaches, Comput. Methods Programs Biomed., 185 (2020), 105169. https://doi.org/10.1016/j.cmpb.2019.105169 doi: 10.1016/j.cmpb.2019.105169
|
| [24] |
X. Wang, G. Akram, M. Sadaf, H. Mariyam, M. Abbas, Soliton Solution of the Peyrard-Bishop-Dauxois Model of DNA Dynamics with M-Truncated and β-Fractional Derivatives Using Kudryashov's R Function Method, Fractal Fract., 6 (2022), 616. https://doi.org/10.3390/fractalfract6100616 doi: 10.3390/fractalfract6100616
|
| [25] | J. B. Okaly, T. Nkoa Nkomom, Nonlinear Dynamics of DNA Chain with Long-Range Interactions, In: Nonlinear Dynamics of Nanobiophysics, Singapore: Springer, 2022. https://doi.org/10.1007/978-981-19-5323-1_4 |
| [26] | A. Bugay, Soliton excitations in a Twist-Opening Nonlinear DNA Model, In: Nonlinear Dynamics of Nanobiophysics, Singapore: Springer, 2022. https://doi.org/10.1007/978-981-19-5323-1_7 |
| [27] | I. Hubac, F. Blaschke, O. N. Karpisek, Quantum information in biomolecules: Transcription and replication of DNA using a soliton model, Opava, Proceedings of RAGtime 22: Workshops on Black Holes and Neutron Stars, 2020, 55–71. |
| [28] | N. Ayyappan, C. M. Joy, L. Kavitha, Stability analysis of DNA with the effect of twist and Morse potential, Mater. Today: Proc., 51 (2022), 1793–1796. |
| [29] |
M. A. Abdou, L. Ouahid, J. S. Al Shahrani, M. M. Alanazi, S. Kumar, New analytical solutions and efficient methodologies for DNA (Double-Chain Model) in mathematical biology, Modern Phys. Lett. B, 36 (2022), 2250124. https://doi.org/10.1142/S021798492250124X doi: 10.1142/S021798492250124X
|
| [30] |
R. Saleh, S. M. Mabrouk, A. M. Wazwaz, Lie symmetry analysis of a stochastic gene evolution in double-chain deoxyribonucleic acid system, Waves Random Complex Media, 32 (2022), 2903–2917. https://doi.org/10.1080/17455030.2020.1871109 doi: 10.1080/17455030.2020.1871109
|
| [31] |
D. Shi, H. U. Rehman, I. Iqbal, M. Vivas-Cortez, M. S. Saleem, X. Zhang, Analytical study of the dynamics in the double-chain model of DNA, Results Phys., 52 (2023), 106787. https://doi.org/10.1016/j.rinp.2023.106787 doi: 10.1016/j.rinp.2023.106787
|
| [32] |
M. Vivas-Cortez, S. Arshed, M. Sadaf, Z. Perveen, G. Akram, Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis, PLoS One, 18 (2023), e0281318. https://doi.org/10.1371/journal.pone.0281318 doi: 10.1371/journal.pone.0281318
|
| [33] |
T. Han, K. Zhang, Y. Jiang, H. Rezazadeh, Chaotic Pattern and Solitary Solutions for the (21)-Dimensional Beta-Fractional Double-Chain DNA System, Fractal Fract., 8 (2024), 415. https://doi.org/10.3390/fractalfract8070415 doi: 10.3390/fractalfract8070415
|
| [34] | N. O. Nfor, Higher order periodic base pairs opening in a finite stacking enthalpy DNA model, J. Modern Phys., 12 (2021), 1843–1865. |
| [35] |
S. W. Yao, S. M. Mabrouk, M. Inc, A. S. Rashed, Analysis of double-chain deoxyribonucleic acid dynamical system in pandemic confrontation, Results Phys., 42 (2022), 105966. https://doi.org/10.1016/j.rinp.2022.105966 doi: 10.1016/j.rinp.2022.105966
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Mostafa M. A. Khater, Mohammed Zakarya, Kottakkaran Sooppy Nisar, Abdel-Haleem Abdel-Aty. Dynamics and stability analysis of nonlinear DNA molecules: Insights from the Peyrard-Bishop model[J]. AIMS Mathematics, 2024, 9(9): 23449-23467. doi: 10.3934/math.20241140
| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
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| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
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| Article type | Number | Percent |
| Research article | 12 | 43% |
| Review | 10 | 36% |
| Others | 6 | 21% |
| Total | 28 |
| Title | Corresponding author | Views | |
| 1 | Knowledge, attitudes on falls and awareness of hospitalized patient's fall risk factors among the nurses working in Tertiary Care Hospitals | Surapaneni Krishna Mohan | 1861 |
| 2 | Clinical pharmacology to support monoclonal antibody drug development | Sharon Lu | 1861 |
| 3 | Telehealth during COVID-19 pandemic era: a systematic review | Jonathan Kissi | 1787 |
| 4 | Understanding the psychological impact of the COVID-19 pandemic on university students | Belgüzar Kara | 1786 |
| 5 | Soluble Fas ligand, soluble Fas receptor, and decoy receptor 3 as disease biomarkers for clinical applications: A review | Michiro Muraki | 1697 |
| 6 | Non-small cell lung cancer: epidemiology, screening, diagnosis, and treatment | Anuj A. Shukla | 1613 |
| 7 | Recurrence after treatment of arteriovenous malformations of the head and neck | Nguyen Minh Duc | 1583 |
| 8 | Staphylococcus aureus antimicrobial efflux pumps and their inhibitors: recent developments | Manuel Varela | 1467 |
| 9 | The mental health of the health care professionals in India during the COVID-19 pandemic: a cross-sectional study | B Shivananda Nayak | 1268 |
| 10 | Recognition, treatment, and prevention of perioperative anaphylaxis: a narrative review | Julena Foglia | 1210 |
