t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.5 |
1 | 39.6912 | 39.5848 | 39.51 | 39.4383 |
1.5 | 39.3299 | 39.1117 | 39.0235 | 39.1181 |
3 | 37.2519 | 36.2268 | 36.264 | 37.5584 |
4.5 | 32.0652 | 29.2568 | 30.0105 | 34.514 |
6 | 19.0984 | 14.0068 | 17.2162 | 29.3074 |
Epileptogenesis is a complex and not well understood phenomenon. Here, we explore the hypothesis that epileptogenesis could be “hijacking” normal memory processes, and how this hypothesis may provide new directions for epilepsy treatment. First, we review similarities between the hypersynchronous circuits observed in epilepsy and memory consolidation processes involved in strengthening neuronal connections. Next, we describe the kindling model of seizures and its relation to long-term potentiation model of synaptic plasticity. We also examine how the strengthening of epileptic circuits is facilitated during the physiological slow wave sleep, similarly as episodic memories. Furthermore, we present studies showing that specific memories can directly trigger reflex seizures. The neuronal hypersynchrony in early stages of Alzheimer's disease, and the use of anti-epileptic drugs to improve the cognitive symptoms in this disease also suggests a connection between memory systems and epilepsy. Given the commonalities between memory processes and epilepsy, we propose that therapies for memory disorders might provide new avenues for treatment of epileptic patients.
Citation: Ritwik Das, Artur Luczak. Epileptic seizures and link to memory processes[J]. AIMS Neuroscience, 2022, 9(1): 114-127. doi: 10.3934/Neuroscience.2022007
[1] | Norliyana Nor Hisham Shah, Rashid Jan, Hassan Ahmad, Normy Norfiza Abdul Razak, Imtiaz Ahmad, Hijaz Ahmad . Enhancing public health strategies for tungiasis: A mathematical approach with fractional derivative. AIMS Bioengineering, 2023, 10(4): 384-405. doi: 10.3934/bioeng.2023023 |
[2] | Rashid Jan, Imtiaz Ahmad, Hijaz Ahmad, Narcisa Vrinceanu, Adrian Gheorghe Hasegan . Insights into dengue transmission modeling: Index of memory, carriers, and vaccination dynamics explored via non-integer derivative. AIMS Bioengineering, 2024, 11(1): 44-65. doi: 10.3934/bioeng.2024004 |
[3] | Honar J. Hamad, Sarbaz H. A. Khoshnaw, Muhammad Shahzad . Model analysis for an HIV infectious disease using elasticity and sensitivity techniques. AIMS Bioengineering, 2024, 11(3): 281-300. doi: 10.3934/bioeng.2024015 |
[4] | Atta Ullah, Hamzah Sakidin, Shehza Gul, Kamal Shah, Yaman Hamed, Maggie Aphane, Thabet Abdeljawad . Sensitivity analysis-based control strategies of a mathematical model for reducing marijuana smoking. AIMS Bioengineering, 2023, 10(4): 491-510. doi: 10.3934/bioeng.2023028 |
[5] | Mehmet Yavuz, Waled Yavız Ahmed Haydar . A new mathematical modelling and parameter estimation of COVID-19: a case study in Iraq. AIMS Bioengineering, 2022, 9(4): 420-446. doi: 10.3934/bioeng.2022030 |
[6] | Fırat Evirgen, Fatma Özköse, Mehmet Yavuz, Necati Özdemir . Real data-based optimal control strategies for assessing the impact of the Omicron variant on heart attacks. AIMS Bioengineering, 2023, 10(3): 218-239. doi: 10.3934/bioeng.2023015 |
[7] | Ayub Ahmed, Bashdar Salam, Mahmud Mohammad, Ali Akgül, Sarbaz H. A. Khoshnaw . Analysis coronavirus disease (COVID-19) model using numerical approaches and logistic model. AIMS Bioengineering, 2020, 7(3): 130-146. doi: 10.3934/bioeng.2020013 |
[8] | Mariem Jelassi, Kayode Oshinubi, Mustapha Rachdi, Jacques Demongeot . Epidemic dynamics on social interaction networks. AIMS Bioengineering, 2022, 9(4): 348-361. doi: 10.3934/bioeng.2022025 |
[9] | Shital Hajare, Rajendra Rewatkar, K.T.V. Reddy . Design of an iterative method for enhanced early prediction of acute coronary syndrome using XAI analysis. AIMS Bioengineering, 2024, 11(3): 301-322. doi: 10.3934/bioeng.2024016 |
[10] | Adam B Fisher, Stephen S Fong . Lignin biodegradation and industrial implications. AIMS Bioengineering, 2014, 1(2): 92-112. doi: 10.3934/bioeng.2014.2.92 |
Epileptogenesis is a complex and not well understood phenomenon. Here, we explore the hypothesis that epileptogenesis could be “hijacking” normal memory processes, and how this hypothesis may provide new directions for epilepsy treatment. First, we review similarities between the hypersynchronous circuits observed in epilepsy and memory consolidation processes involved in strengthening neuronal connections. Next, we describe the kindling model of seizures and its relation to long-term potentiation model of synaptic plasticity. We also examine how the strengthening of epileptic circuits is facilitated during the physiological slow wave sleep, similarly as episodic memories. Furthermore, we present studies showing that specific memories can directly trigger reflex seizures. The neuronal hypersynchrony in early stages of Alzheimer's disease, and the use of anti-epileptic drugs to improve the cognitive symptoms in this disease also suggests a connection between memory systems and epilepsy. Given the commonalities between memory processes and epilepsy, we propose that therapies for memory disorders might provide new avenues for treatment of epileptic patients.
In 2014, an outbreak of Ebola virus (Ebola) decimated many people in Western Africa. With more than 16,000 clinically confirmed cases and approximately 70% mortality cases, this was the more deadly outbreak compared to 20 Ebola threats that occurred since 1976 [1]. In Africa, and particularly in the regions that were affected by Ebola outbreaks, people live close to the rain-forests, hunt bats and monkeys and harvest forest fruits for food [2], [3].
In [4] develop a SIR type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses with stability and numerical analysis is discussed. A number of mathematical models have been developed to understand the transmission dynamics of Ebola and other infectious diseases outbreak from various aspects [5], [6]. A commonly used model for characterising epidemics of diseases including Ebola is the susceptible-exposed-infectious-recovered (SEIR) model [7], and extensions to this basic model include explicit incorporation of transmission from Ebola deceased hosts [1], [8] or accounting for mismatches between symptoms and infectiousness [9], [10].
Many researchers and mathematicians have shown that fractional extensions of mathematical integer-order models are a very systematic representation of natural reality [11], [12], [13]. Recently, a non-integer-order idea is given by Caputo and Fabrizio [14]. The primary goal of this article is to use a fresh non-integer order derivative to study the model of diabetes and to present information about the diabetes model solution's uniqueness and existence using a fixed point theorem [15]. Atangana and Baleanu [16] then proposed another non-singular derivative version using the Mittag Leffler kernel function. In many apps in the actual globe, these operators have been successful [17], [18], [19]. The few existing works [4], [8], [9], [20] on the mathematical modeling tells transmission of the virus and spread of Ebola virus on the population of human. The classical settings of mathematical studies tells about spread of EVD, such as SI model, SIR model, SEIR model [4], SEIRD model, or SEIRHD model. World medical association invented medicines for Ebola virus. Quantitative approaches and obtaining an analysis of the reproduction number of Ebola outbreak were important modeling for EVD epidemics. Demographic data on Ebola risk factors and on the transmission of virus were studied through the household structured epidemic model [4], [21]. Predications, different valuable insights, personal and genomic data for EVD was reported and discovered through mathematical models [22], [23]. In [24], the authors observed spread that follows a fading memory process and also shows crossover behaviour for the EVD. They captured this kind of spread using differential operators that posses crossover properties and fading memory using the SIRDP model in [4]. They also analyzed the Ebola disease dynamic by considering the Caputo, Caputo-Fabrizio, and Atangana-Baleanu differential operators.
In this paper, we developed fractional order Ebola virus model by using the Caputo method of complex nonlinear differential equations. Caputo fractional derivative operator β ∈ (0,1] works to achieve the fractional differential equations. Laplace with Adomian Decomposition Methodsuccessfully solved the fractional differential equations. Ultimately, numerical simulations are also developed to evaluate the effects of the device parameter on spread of disease and effect of fractional parameter β on obtained solution which are also assessed by tabulated results.
The classical model for Ebola virus model is given in
Here system (2.1) is analyzed qualitatively analyzed for feasibility and numerical solution at disease free and endemic equilibrium point. For this purpose, we used
Theorem. 1 There is a unique solution for the initial value problem given in system (2.1), and the solution remains in R5, x ≥ 0.
Proof: We need to show that the domain R5, x ≥ 0 is positively invariant. Since
Consider the fractional-order Ebola virus model (2.1), by using Caputo definition with Laplace transform, we have
We get the followings generalized form for analysis and numerical solution.
The results of fractional order model (2.1) is represented in followings tables and graphs.
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.5 |
1 | 39.6912 | 39.5848 | 39.51 | 39.4383 |
1.5 | 39.3299 | 39.1117 | 39.0235 | 39.1181 |
3 | 37.2519 | 36.2268 | 36.264 | 37.5584 |
4.5 | 32.0652 | 29.2568 | 30.0105 | 34.514 |
6 | 19.0984 | 14.0068 | 17.2162 | 29.3074 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
1 | 10.4879 | 10.6026 | 10.6542 | 10.7698 |
2 | 12.052 | 11.9378 | 11.8579 | 11.5689 |
4 | 13.2768 | 12.5387 | 12.2499 | 11.8581 |
6 | 8.7256 | 9.97166 | 10.5704 | 12.7973 |
8 | 5.0464 | 11.4457 | 13.7013 | 19.4353 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
2 | 20.504 | 20.5195 | 20.5331 | 20.5414 |
4 | 21.952 | 21.8288 | 21.6815 | 21.509 |
6 | 25.448 | 24.6081 | 23.8154 | 23.076 |
8 | 32.096 | 29.4003 | 27.1489 | 25.2921 |
10 | 43 | 36.6889 | 31.8489 | 28.1877 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
0.5 | 10.5931 | 10.6768 | 10.7803 | 10.9131 |
1 | 11.3486 | 11.5116 | 11.7127 | 11.9551 |
1.5 | 12.531 | 12.8083 | 13.1141 | 13.4308 |
2 | 14.4048 | 14.7773 | 15.124 | 15.4064 |
t | ϕ = 1 | ϕ = 0.95 | ϕ = 0.9 | ϕ = 0.85 |
1 | 5.67835 | 5.6959 | 5.68235 | 5.7302 |
2 | 6.4746 | 6.46707 | 6.45834 | 6.44629 |
4 | 8.788 | 8.62982 | 8.47227 | 8.30553 |
6 | 12.6746 | 12.1038 | 11.562 | 11.0225 |
8 | 18.8688 | 17.417 | 16.0958 | 14.8435 |
10 | 28.105 | 25.0658 | 22.3972 | 19.9683 |
The objective of our work is to develop a scheme of epidemic fractional Ebola virus model with Caputo fractional derivative also numerical solutions have been obtained by using the Laplace with the Adomian Decomposition Method. The results of fractional order Ebola virus model is presented and convergence results of fractional-order model are also presented to demonstrate the efficacy of the process. The analytical solution of the fractional-order Ebola virus model consisting of the non-linear system of the fractional differential equation has been presented by using the Caputo derivative. To observe the effects of the fractional parameter on the dynamics of the fractional-order model (2.1), we conclude several numerical simulations varying the values of parameter given in [4]. These simulations reveal that a change in the value affects the dynamics of the model. The numerical solutions at classical as well as different fractional values by using Caputo fractional derivative can be seen in Figures 1–5 for disease free equilibrium. The rate of susceptible individuals and pathogens decreases by reducing the fractional values to acquire the desired value, whereas the other compartment starts decreasing by increasing the fractional values. The fractional-order model shows the convergence with theoretical contribution and numerical results. The fractional-order parameter values show the impact of increasing or decreasing the disease. Also, we can fix the parameter values where the rate of infection is decrease and the recover rate will increase for some values which are representing in figures and tables. These results can be used for disease outbreak treatment and analysis without defining the control parameters in the model based on fractional values. In general, approaches to fractional-order modeling in situations with large refined data sets and good numerical algorithms may be worth it. The simulation and numerical solutions at classical as well as different fractional values by using Caputo fractional derivative can be seen in Figures 6–10 for endemic equilibrium as well as in Tables 1–5. Results in both cases are reliable at fractional values to overcome the outbreak of this epidemic and meet our desired accuracy. Results discuss in [1], [5] for classical model, but our results are on fractional order model, fractional parameters easily use to adjust the control strategy without defining others parameters in the model. Another important feature that plays a critical role in the 2014 EVD outbreaks is traditional/cultural belief systems and customs. For instance, while some individuals in the three Ebola-stricken nations believe that there is no Ebola, control the population or harvest human organs. We conclude that depending on the specific data set, the fractional order model either converges to the ordinary differential equation model and fits data similarly, or fits the data better and outperforms the ODE model.
We develop a scheme of epidemic fractional Ebola virus model with Caputo fractional derivative for numerical solutions that have been obtained by using the Laplace with the Adomian Decomposition Method. In [24] the use of three different fractional operators on the Ebola disease model suggests that the fractional-order parameter greatly affects disease elimination for the non-integer case when decreasing α. We constructed a numerical solution for the Ebola virus model to show a good agreement to control the bad impact of the Ebola virus for the different period for diseases free and endemic equilibrium point as well. However, in this work, we introduced the qualitative properties for solutions as well as the non-negative unique solution for a fractional-order nonlinear system. It is important to note that the Laplace Adomian Decomposition Method is used for the Ebola virus fractional-order model differential equation framework is a more efficient approach to computing convergent solutions that are represented through figures and tables for endemic and disease-free equilibrium point. Convergence results of the fractional-order model are also presented to demonstrate the efficacy of the process. The techniques developed to provide good results which are useful for understanding the Zika Virus outbreak in our community. It is worthy to observe that fractional derivative shows significant changes and memory effects as compare to ordinary derivatives. This model will assist the public health planar in framing an Ebola virus disease control policy. Also, we will expand the model incorporating determinist and stochastic model comparisons with fractional technique, as well as using optimal control theory for new outcomes.
[1] |
Wilson MA, McNaughton BL (1994) Reactivation of hippocampal ensemble memories during sleep. Science 265: 676-679. https://doi.org/10.1126/science.8036517 ![]() |
[2] |
Beenhakker MP, Huguenard JR (2009) Neurons that Fire Together Also Conspire Together: Is Normal Sleep Circuitry Hijacked to Generate Epilepsy?. Neuron 62: 612-632. https://doi.org/10.1016/j.neuron.2009.05.015 ![]() |
[3] |
Neumann AR, Raedt R, Steenland HW, et al. (2017) Involvement of fast-spiking cells in ictal sequences during spontaneous seizures in rats with chronic temporal lobe epilepsy. Brain 140: 2355-2369. https://doi.org/10.1093/brain/awx179 ![]() |
[4] |
Matos G, Tufik S, Scorza FA, et al. (2011) Sleep, epilepsy and translational research: What can we learn from the laboratory bench?. Prog Neurobiol 95: 396-405. https://doi.org/10.1016/j.pneurobio.2011.09.006 ![]() |
[5] |
Karoly PJ, Rao VR, Gregg NM, et al. (2021) Cycles in epilepsy. Nat Rev Neurol 17: 267-284. https://doi.org/10.1038/s41582-021-00464-1 ![]() |
[6] |
Amengual-Gual M, Sánchez Fernández I, Loddenkemper T (2019) Patterns of epileptic seizure occurrence. Brain Res 1703: 3-12. https://doi.org/10.1016/j.brainres.2018.02.032 ![]() |
[7] |
Gupta AK, Jeavons PM, Hughes RC, et al. (1983) Aura in temporal lobe epilepsy: clinical and electroencephalographic correlation. J Neurol Neurosur Ps 46: 1079-1083. https://doi.org/10.1136/jnnp.46.12.1079 ![]() |
[8] | Boada C, Grossman S, Dugan P, et al. (2020) Aura Semiology as a Predictor of Outcomes Following Epilepsy Surgery (634). Neurology 94. |
[9] |
Engel J (2001) A Proposed Diagnostic Scheme for People with Epileptic Seizures and with Epilepsy: Report of the ILAE Task Force on Classification and Terminology. Epilepsia 42: 796-803. https://doi.org/10.1046/j.1528-1157.2001.10401.x ![]() |
[10] |
Engel J (2006) ILAE classification of epilepsy syndromes. Epilepsy Res 70: 5-10. https://doi.org/10.1016/j.eplepsyres.2005.11.014 ![]() |
[11] |
Fisher RS, Cross JH, D'Souza C, et al. (2017) Instruction manual for the ILAE 2017 operational classification of seizure types. Epilepsia 58: 531-542. https://doi.org/10.1111/epi.13671 ![]() |
[12] |
Koutroumanidis M, Panayiotopoulos C (2004) Reflex seizures and reflex epilepsies. Epilepsy in Children, 2E.CRC Press 243-249. https://doi.org/10.1201/b13560-36 ![]() |
[13] |
Xue LY, Ritaccio AL (2006) Reflex Seizures and Reflex Epilepsy. Am J Electroneurodiagnostic Technol 46: 39-48. https://doi.org/10.1080/1086508X.2006.11079556 ![]() |
[14] |
Navarro V, Adam C, Petitmengin C, et al. (2006) Toothbrush-Thinking Seizures. Epilepsia 47: 1971-1973. https://doi.org/10.1111/j.1528-1167.2006.00822.x ![]() |
[15] |
Irmen F, Wehner T, Lemieux L (2015) Do reflex seizures and spontaneous seizures form a continuum?—Triggering factors and possible common mechanisms. Seizure 25: 72-79. https://doi.org/10.1016/j.seizure.2014.12.006 ![]() |
[16] |
Nguyen PV, Abel T, Kandel ER (1994) Requirement of a Critical Period of Transcription for Induction of a Late Phase of LTP. Science 265: 1104-1107. https://doi.org/10.1126/science.8066450 ![]() |
[17] |
Palop JJ, Chin J, Roberson ED, et al. (2007) Aberrant Excitatory Neuronal Activity and Compensatory Remodeling of Inhibitory Hippocampal Circuits in Mouse Models of Alzheimer's Disease. Neuron 55: 697-711. https://doi.org/10.1016/j.neuron.2007.07.025 ![]() |
[18] |
Bower MR, Stead M, Bower RS, et al. (2015) Evidence for Consolidation of Neuronal Assemblies after Seizures in Humans. J Neurosci 35: 999-1010. https://doi.org/10.1523/JNEUROSCI.3019-14.2015 ![]() |
[19] |
de Curtis M, Avanzini G (2001) Interictal spikes in focal epileptogenesis. Prog Neurobiol 63: 541-567. https://doi.org/10.1016/S0301-0082(00)00026-5 ![]() |
[20] |
Bower MR, Kucewicz MT, st. Louis EK, et al. (2017) Reactivation of seizure-related changes to interictal spike shape and synchrony during postseizure sleep in patients. Epilepsia 58: 94-104. https://doi.org/10.1111/epi.13614 ![]() |
[21] |
Del Felice A, Storti SF, Manganotti P (2015) Sleep affects cortical source modularity in temporal lobe epilepsy: A high-density EEG study. Clin Neurophysiol 126: 1677-1683. https://doi.org/10.1016/j.clinph.2014.12.003 ![]() |
[22] |
Lambert I, Roehri N, Giusiano B, et al. (2018) Brain regions and epileptogenicity influence epileptic interictal spike production and propagation during NREM sleep in comparison with wakefulness. Epilepsia 59: 235-243. https://doi.org/10.1111/epi.13958 ![]() |
[23] |
Sparks FT, Liao Z, Li W, et al. (2020) Hippocampal adult-born granule cells drive network activity in a mouse model of chronic temporal lobe epilepsy. Nat Commun 11: 6138. https://doi.org/10.1038/s41467-020-19969-2 ![]() |
[24] |
Georgopoulou V, Spruyt K, Garganis K, et al. (2021) Altered Sleep-Related Consolidation and Neurocognitive Comorbidity in CECTS. Front Hum Neurosci 15: 244. https://doi.org/10.3389/fnhum.2021.563807 ![]() |
[25] |
Halász P, Bódizs R, Ujma PP, et al. (2019) Strong relationship between NREM sleep, epilepsy and plastic functions—A conceptual review on the neurophysiology background. Epilepsy Res 150: 95-105. https://doi.org/10.1016/j.eplepsyres.2018.11.008 ![]() |
[26] | Hahn MA, Heib D, Schabus M, et al. (2020) Slow oscillation-spindle coupling predicts enhanced memory formation from childhood to adolescence. eLife 9: 1-21. https://doi.org/10.7554/eLife.53730 |
[27] |
Stickgold R (2005) Sleep-dependent memory consolidation. Nature 437: 1272-1278. https://doi.org/10.1038/nature04286 ![]() |
[28] |
Buzsáki G (1996) The Hippocampo-Neocortical Dialogue. Cereb Cortex 6: 81-92. https://doi.org/10.1093/cercor/6.2.81 ![]() |
[29] |
McClelland JL, McNaughton B, O'Reilly R (1995) Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory. Psychol Rev 102 3: 419-457. https://doi.org/10.1037/0033-295X.102.3.419 ![]() |
[30] |
Squire LR (2004) Memory systems of the brain: A brief history and current perspective. Neurobiol Learn Mem 82: 171-177. https://doi.org/10.1016/j.nlm.2004.06.005 ![]() |
[31] |
Gelinas JN, Khodagholy D, Thesen T, et al. (2016) Interictal epileptiform discharges induce hippocampal–cortical coupling in temporal lobe epilepsy. Nat Med 22: 641-648. https://doi.org/10.1038/nm.4084 ![]() |
[32] |
Kleen JK, Scott RC, Holmes GL, et al. (2010) Hippocampal interictal spikes disrupt cognition in rats. Ann Neurol 67: 250-257. https://doi.org/10.1002/ana.21896 ![]() |
[33] |
Kleen JK, Scott RC, Holmes GL, et al. (2013) Hippocampal interictal epileptiform activity disrupts cognition in humans. Neurology 81: 18-24. https://doi.org/10.1212/WNL.0b013e318297ee50 ![]() |
[34] |
Lambert I, Tramoni-Negre E, Lagarde S, et al. (2020) Hippocampal Interictal Spikes during Sleep Impact Long-Term Memory Consolidation. Ann Neurol 87: 976-987. https://doi.org/10.1002/ana.25744 ![]() |
[35] |
Lambert I, Tramoni-Negre E, Lagarde S, et al. (2021) Accelerated long-term forgetting in focal epilepsy: Do interictal spikes during sleep matter?. Epilepsia 62: 563-569. https://doi.org/10.1111/epi.16823 ![]() |
[36] |
Maharathi B, Wlodarski R, Bagla S, et al. (2019) Interictal spike connectivity in human epileptic neocortex. Clin Neurophysiol 130: 270-279. https://doi.org/10.1016/j.clinph.2018.11.025 ![]() |
[37] |
Arbune AA, Meritam Larsen P, Wüstenhagen S, et al. (2021) Modulation in time of the interictal spiking pattern related to epileptic seizures. Clin Neurophysiol 132: 1083-1088. https://doi.org/10.1016/j.clinph.2021.01.026 ![]() |
[38] |
Buzsáki G (2015) Hippocampal sharp wave-ripple: A cognitive biomarker for episodic memory and planning. Hippocampus 25: 1073-1188. https://doi.org/10.1002/hipo.22488 ![]() |
[39] |
Jacobs J, Zijlmans M, Zelmann R, et al. (2010) High-frequency electroencephalographic oscillations correlate with outcome of epilepsy surgery. Ann Neurol 67: 209-220. https://doi.org/10.1002/ana.21847 ![]() |
[40] |
Jacobs J, LeVan P, Chander R, et al. (2008) Interictal high-frequency oscillations (80–500 Hz) are an indicator of seizure onset areas independent of spikes in the human epileptic brain. Epilepsia 49: 1893-1907. https://doi.org/10.1111/j.1528-1167.2008.01656.x ![]() |
[41] |
Jacobs J, Banks S, Zelmann R, et al. (2016) Spontaneous ripples in the hippocampus correlate with epileptogenicity and not memory function in patients with refractory epilepsy. Epilepsy Behav 62: 258-266. https://doi.org/10.1016/j.yebeh.2016.05.025 ![]() |
[42] | Liu S, Parvizi J (2019) Cognitive refractory state caused by spontaneous epileptic high-frequency oscillations in the human brain. Sci Transl Med 11. https://doi.org/10.1126/scitranslmed.aax7830 |
[43] |
Ewell LA, Fischer KB, Leibold C, et al. (2019) The impact of pathological high-frequency oscillations on hippocampal network activity in rats with chronic epilepsy. eLife 8. https://doi.org/10.7554/eLife.42148 ![]() |
[44] |
Karlócai MR, Kohus Z, Káli S, et al. (2014) Physiological sharp wave-ripples and interictal events in vitro: what's the difference?. Brain 137: 463-485. https://doi.org/10.1093/brain/awt348 ![]() |
[45] | Augusto R, Mendes V, Zacharias LR, et al. Hijacking of hippocampal-cortical oscillatory coupling during sleep in temporal lobe epilepsy (2019)121: 106608. https://doi.org/10.1016/j.yebeh.2019.106608 |
[46] | Teskey GC (2020) Kindling. Oxford Research Encyclopedia of Psychology . https://doi.org/10.1093/acrefore/9780190236557.013.790 |
[47] |
Goddard G v (1967) Development of Epileptic Seizures through Brain Stimulation at Low Intensity. Nature 214: 1020-1021. https://doi.org/10.1038/2141020a0 ![]() |
[48] |
Marescaux C, Vergnes M, Kiesmann M, et al. (1987) Kindling of audiogenic seizures in Wistar rats: An EEG study. Exp Neurol 97: 160-168. https://doi.org/10.1016/0014-4886(87)90290-1 ![]() |
[49] |
Cela E, McFarlan AR, Chung AJ, et al. (2019) An Optogenetic Kindling Model of Neocortical Epilepsy. Sci Rep 9: 1-12. https://doi.org/10.1038/s41598-019-41533-2 ![]() |
[50] | Shimada T, Yamagata K (2018) Pentylenetetrazole-induced kindling mouse model. J Vis Exp 2018. https://doi.org/10.3791/56573 |
[51] |
McIntyre DC, Poulter MO, Gilby K (2002) Kindling: some old and some new. Epilepsy Res 50: 79-92. https://doi.org/10.1016/S0920-1211(02)00071-2 ![]() |
[52] |
Racine RJ (1972) Modification of seizure activity by electrical stimulation: II. Motor seizure. Electroencephalography Clin Neurophysiol 32: 281-294. https://doi.org/10.1016/0013-4694(72)90177-0 ![]() |
[53] |
Goddard G v, Douglas RM (1975) Does the engram of kindling model the engram of normal long term memory?. Can J Neurol Sci 2: 385-394. https://doi.org/10.1017/S0317167100020539 ![]() |
[54] |
Goddard G v, McIntyre DC, Leech CK (1969) A permanent change in brain function resulting from daily electrical stimulation. Exp Neurol 25: 295-330. https://doi.org/10.1016/0014-4886(69)90128-9 ![]() |
[55] |
Kundap UP, Paudel YN, Kumari Y, et al. (2019) Embelin prevents seizure and associated cognitive impairments in a pentylenetetrazole-induced kindling zebrafish model. Front Pharmacol 10: 315. https://doi.org/10.3389/fphar.2019.00315 ![]() |
[56] |
Metcalf CS, Huff J, Thomson KE, et al. (2019) Evaluation of antiseizure drug efficacy and tolerability in the rat lamotrigine-resistant amygdala kindling model. Epilepsia Open 4: 452-463. https://doi.org/10.1002/epi4.12354 ![]() |
[57] |
Wada JA (1977) Pharmacological Prophylaxis in the Kindling Model of Epilepsy. Arch Neurol 34: 389-395. https://doi.org/10.1001/archneur.1977.00500190023003 ![]() |
[58] |
McNamara JO (1989) Development of New Pharmacological Agents for Epilepsy: Lessons from the Kindling Model. Epilepsia 30: S13-S18. https://doi.org/10.1111/j.1528-1157.1989.tb05809.x ![]() |
[59] |
Mody I, Heinemann U (1987) NMDA receptors of dentate gyrus granule cells participate in synaptic transmission following kindling. Nature 326: 701-704. https://doi.org/10.1038/326701a0 ![]() |
[60] |
Lynch M, Sayin Ü, Golarai G, et al. (2000) NMDA Receptor-Dependent Plasticity of Granule Cell Spiking in the Dentate Gyrus of Normal and Epileptic Rats. J Neurophysiol 84: 2868-2879. https://doi.org/10.1152/jn.2000.84.6.2868 ![]() |
[61] |
Dalby NO, Mody I (2003) Activation of NMDA Receptors in Rat Dentate Gyrus Granule Cells by Spontaneous and Evoked Transmitter Release. J Neurophysiol 90: 786-797. https://doi.org/10.1152/jn.00118.2003 ![]() |
[62] |
Bliss TVP, Collingridge GL, Morris RGM, et al. (2018) Long-term potentiation in the hippocampus: discovery, mechanisms and function. Neuroforum 24: A103-A120. https://doi.org/10.1515/nf-2017-A059 ![]() |
[63] |
Citri A, Malenka RC (2008) Synaptic Plasticity: Multiple Forms, Functions, and Mechanisms. Neuropsychopharmacology 33: 18-41. https://doi.org/10.1038/sj.npp.1301559 ![]() |
[64] |
Malenka RC, Nicoll RA (1999) Long-Term Potentiation--A Decade of Progress?. Science 285: 1870-1874. https://doi.org/10.1126/science.285.5435.1870 ![]() |
[65] |
Abraham WC, Jones OD, Glanzman DL (2019) Is plasticity of synapses the mechanism of long-term memory storage?. npj Sci Learn 4: 9. https://doi.org/10.1038/s41539-019-0048-y ![]() |
[66] |
Bliss TVP, Collingridge GL (1993) A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361: 31-39. https://doi.org/10.1038/361031a0 ![]() |
[67] |
Lømo T (2003) The discovery of long-term potentiation. Philos T Roy Soc B 358: 617-620. https://doi.org/10.1098/rstb.2002.1226 ![]() |
[68] |
Nicoll RA (2017) A Brief History of Long-Term Potentiation. Neuron 93: 281-290. https://doi.org/10.1016/j.neuron.2016.12.015 ![]() |
[69] |
Kauer JA, Malenka RC, Nicoll RA (1988) A persistent postsynaptic modification mediates long-term potentiation in the hippocampus. Neuron 1: 911-917. https://doi.org/10.1016/0896-6273(88)90148-1 ![]() |
[70] |
Ruan Y, Xu C, Lan J, et al. (2020) Low-frequency Stimulation at the Subiculum is Anti-convulsant and Anti-drug-resistant in a Mouse Model of Lamotrigine-resistant Temporal Lobe Epilepsy. Neurosci Bull 36: 654. https://doi.org/10.1007/s12264-020-00482-x ![]() |
[71] |
Mihály I, Orbán-Kis K, Gáll Z, et al. (2020) Amygdala low-frequency stimulation reduces pathological phase-amplitude coupling in the pilocarpine model of epilepsy. Brain Sci 10: 1-18. https://doi.org/10.3390/brainsci10110856 ![]() |
[72] |
Paschen E, Elgueta C, Heining K, et al. (2020) Hippocampal low-frequency stimulation prevents seizure generation in a mouse model of mesial temporal lobe epilepsy. eLife 9: 1-57. https://doi.org/10.7554/eLife.54518 ![]() |
[73] |
Albensi BC, Ata G, Schmidt E, et al. (2004) Activation of long-term synaptic plasticity causes suppression of epileptiform activity in rat hippocampal slices. Brain Res 998: 56-64. https://doi.org/10.1016/j.brainres.2003.11.010 ![]() |
[74] |
Velı́šek L, Velı́šková J, Stanton PK (2002) Low-frequency stimulation of the kindling focus delays basolateral amygdala kindling in immature rats. Neurosci Lett 326: 61-63. https://doi.org/10.1016/S0304-3940(02)00294-X ![]() |
[75] |
Wagner JJ, Alger BE (1996) Homosynaptic LTD and depotentiation: Do they differ in name only?. Hippocampus 6: 24-29. https://doi.org/10.1002/(SICI)1098-1063(1996)6:1<24::AID-HIPO5>3.0.CO;2-7 ![]() |
[76] |
Chapman KB, Yousef TA, Foster A, et al. (2021) Mechanisms for the Clinical Utility of Low-Frequency Stimulation in Neuromodulation of the Dorsal Root Ganglion. Neuromodulation: Technology at the Neural Interface 24: 738-745. https://doi.org/10.1111/ner.13323 ![]() |
[77] |
Nicholls RE, Alarcon JM, Malleret G, et al. (2008) Transgenic Mice Lacking NMDAR-Dependent LTD Exhibit Deficits in Behavioral Flexibility. Neuron 58: 104-117. https://doi.org/10.1016/j.neuron.2008.01.039 ![]() |
[78] |
Malleret G, Alarcon JM, Martel G, et al. (2010) Bidirectional Regulation of Hippocampal Long-Term Synaptic Plasticity and Its Influence on Opposing Forms of Memory. J Neurosci 30: 3813-3825. https://doi.org/10.1523/JNEUROSCI.1330-09.2010 ![]() |
[79] |
Palop JJ, Mucke L (2016) Network abnormalities and interneuron dysfunction in Alzheimer disease. Nat Rev Neurosci 17: 777-792. https://doi.org/10.1038/nrn.2016.141 ![]() |
[80] |
Sasaguri H, Nilsson P, Hashimoto S, et al. (2017) APP mouse models for Alzheimer's disease preclinical studies. EMBO J 36: 2473-2487. https://doi.org/10.15252/embj.201797397 ![]() |
[81] |
Bezzina C, Verret L, Juan C, et al. (2015) Early onset of hypersynchronous network activity and expression of a marker of chronic seizures in the Tg2576 mouse model of Alzheimer's disease. PLoS ONE 10. https://doi.org/10.1371/journal.pone.0119910 ![]() |
[82] |
Busche MA, Konnerth A (2016) Impairments of neural circuit function in Alzheimer's disease. Philos T Roy Soc B 371. https://doi.org/10.1098/rstb.2015.0429 ![]() |
[83] |
Ramírez-Toraño F, García-Alba J, Bruña R, et al. (2021) Hypersynchronized Magnetoencephalography Brain Networks in Patients with Mild Cognitive Impairment and Alzheimer's Disease in down Syndrome. Brain Connect 11: 725-733. https://doi.org/10.1089/brain.2020.0897 ![]() |
[84] |
Noebels J (2011) A perfect storm: Converging paths of epilepsy and Alzheimer's dementia intersect in the hippocampal formation. Epilepsia 52: 39-46. https://doi.org/10.1111/j.1528-1167.2010.02909.x ![]() |
[85] |
Yassa MA, Stark SM, Bakker A, et al. (2010) High-resolution structural and functional MRI of hippocampal CA3 and dentate gyrus in patients with amnestic Mild Cognitive Impairment. NeuroImage 51: 1242-1252. https://doi.org/10.1016/j.neuroimage.2010.03.040 ![]() |
[86] |
Lam AD, Deck G, Goldman A, et al. (2017) Silent hippocampal seizures and spikes identified by foramen ovale electrodes in Alzheimer's disease. Nat Med 23: 678-680. https://doi.org/10.1038/nm.4330 ![]() |
[87] |
Wilson IA, Gallagher M, Eichenbaum H, et al. (2006) Neurocognitive aging: prior memories hinder new hippocampal encoding. Trends Neurosci 29: 662-670. https://doi.org/10.1016/j.tins.2006.10.002 ![]() |
[88] |
Leppik IE, Birnbaum AK (2010) Epilepsy in the Elderly. Ann NY Acad Sci 1184: 208. https://doi.org/10.1111/j.1749-6632.2009.05113.x ![]() |
[89] |
Olafsson E, Ludvigsson P, Gudmundsson G, et al. (2005) Incidence of unprovoked seizures and epilepsy in Iceland and assessment of the epilepsy syndrome classification: a prospective study. Lancet Neurol 4: 627-634. https://doi.org/10.1016/S1474-4422(05)70172-1 ![]() |
[90] |
Liu D, Lu H, Stein E, et al. (2018) Brain regional synchronous activity predicts tauopathy in 3×TgAD mice. Neurobiol Aging 70: 160-169. https://doi.org/10.1016/j.neurobiolaging.2018.06.016 ![]() |
[91] |
Jacob L, Bohlken J, Schmitz B, et al. (2019) Incidence of epilepsy and associated factors in elderly patients in Germany. Epilepsy Behav 90: 107-111. https://doi.org/10.1016/j.yebeh.2018.10.035 ![]() |
[92] |
Koh MT, Haberman RP, Foti S, et al. (2010) Treatment Strategies Targeting Excess Hippocampal Activity Benefit Aged Rats with Cognitive Impairment. Neuropsychopharmacology 35: 1016-1025. https://doi.org/10.1038/npp.2009.207 ![]() |
[93] | Sanchez PE, Zhu L, Verret L, et al. (2012) Levetiracetam suppresses neuronal network dysfunction and reverses synaptic and cognitive deficits in an Alzheimer's disease model. P Natl Acad Sci 109: E2895 LP-E2903. https://doi.org/10.1073/pnas.1121081109 |
[94] |
Wolf P (2017) Reflex epileptic mechanisms in humans: Lessons about natural ictogenesis. Epilepsy Behav 71: 118-123. https://doi.org/10.1016/j.yebeh.2015.01.009 ![]() |
[95] | Wieser HG (1998) Seizure induction in reflex seizures and reflex epilepsy. Adv Neurol 75: 69-85. |
[96] | Arslan Y, Yilmaz Z, Mülayim S, et al. (2013) Eating Epilepsy After Resection of Frontal Meningioma: A Case Report. Arch Epilepsy 19: 85-89. https://doi.org/10.5505/epilepsi.2013.19483 |
[97] |
Ferlazzo E, Zifkin BG, Andermann E, et al. (2005) Cortical triggers in generalized reflex seizures and epilepsies. Brain 128: 700-710. https://doi.org/10.1093/brain/awh446 ![]() |
[98] |
Szűcs A, Rosdy B, Kelemen A, et al. (2019) Reflex seizure triggering: Learning about seizure producing systems. Seizure 69: 25-30. https://doi.org/10.1016/j.seizure.2019.03.019 ![]() |
[99] |
Falip M, Rodriguez-Bel L, Castañer S, et al. (2018) Musicogenic reflex seizures in epilepsy with glutamic acid decarbocylase antibodies. Acta Neurol Scand 137: 272-276. https://doi.org/10.1111/ane.12799 ![]() |
[100] | Gelisse P, Thomas P, Padovani R, et al. (2003) Ictal SPECT in a case of pure musicogenic epilepsy. Epileptic Disord 5: 133-137. |
[101] | Jallon P, Heraut LA, Vanelle JM (1989) Musicogenic epilepsy. Reflex Seizures and Reflex Epilepsies, Editions Médicine et Hygiène, Geneva : 269-274. |
[102] |
Tezer FI, Bilginer B, Oguz KK, et al. (2014) Musicogenic and spontaneous seizures: EEG analyses with hippocampal depth electrodes. Epileptic Disord 16: 500-505. https://doi.org/10.1684/epd.2014.0706 ![]() |
[103] |
Luczak A, McNaughton BL, Harris KD (2015) Packet-based communication in the cortex. Nat Rev Neurosci 16: 745-755. https://doi.org/10.1038/nrn4026 ![]() |
[104] |
Luczak A, Barthó P, Harris KD (2009) Spontaneous Events Outline the Realm of Possible Sensory Responses in Neocortical Populations. Neuron 62: 413-425. https://doi.org/10.1016/j.neuron.2009.03.014 ![]() |
[105] |
Bortel A, Yao ZS, Shmuel A (2019) A rat model of somatosensory-evoked reflex seizures induced by peripheral stimulation. Epilepsy Res 157: 106209. https://doi.org/10.1016/j.eplepsyres.2019.106209 ![]() |
[106] |
Boly M, Jones B, Findlay G, et al. (2017) Altered sleep homeostasis correlates with cognitive impairment in patients with focal epilepsy. Brain 140: 1026-1040. https://doi.org/10.1093/brain/awx017 ![]() |
[107] |
Sitnikova E, Grubov V, Hramov AE (2020) Slow-wave activity preceding the onset of 10–15-Hz sleep spindles and 5–9-Hz oscillations in electroencephalograms in rats with and without absence seizures. J Sleep Res 29: e12927. https://doi.org/10.1111/jsr.12927 ![]() |
[108] |
van Luijtelaar G, Hramov A, Sitnikova E, et al. (2011) Spike–wave discharges in WAG/Rij rats are preceded by delta and theta precursor activity in cortex and thalamus. Clin Neurophysiol 122: 687-695. https://doi.org/10.1016/j.clinph.2010.10.038 ![]() |
[109] |
Silva BA, Astori S, Burns AM, et al. (2021) A thalamo-amygdalar circuit underlying the extinction of remote fear memories. Nat Neurosci 24: 964-974. https://doi.org/10.1038/s41593-021-00856-y ![]() |
[110] |
Genzel L, Dragoi G, Frank L, et al. (2020) A consensus statement: defining terms for reactivation analysis. Philos T Roy Soc B 375: 20200001. https://doi.org/10.1098/rstb.2020.0001 ![]() |
[111] |
Nader K, Schafe GE, Le Doux JE (2000) Fear memories require protein synthesis in the amygdala for reconsolidation after retrieval. Nature 406: 722-726. https://doi.org/10.1038/35021052 ![]() |
[112] |
Winters BD, Tucci MC, DaCosta-Furtado M (2009) Older and stronger object memories are selectively destabilized by reactivation in the presence of new information. Learn Memory 16: 545-553. https://doi.org/10.1101/lm.1509909 ![]() |
[113] |
Simon KCNS, Gómez RL, Nadel L (2018) Losing memories during sleep after targeted memory reactivation. Neurobiol Learn Mem 151: 10-17. https://doi.org/10.1016/j.nlm.2018.03.003 ![]() |
[114] |
Brunet A, Saumier D, Liu A, et al. (2018) Reduction of PTSD Symptoms With Pre-Reactivation Propranolol Therapy: A Randomized Controlled Trial. Am J Psychiat 175: 427-433. https://doi.org/10.1176/appi.ajp.2017.17050481 ![]() |
[115] |
Schwabe L, Nader K, Wolf OT, et al. (2012) Neural Signature of Reconsolidation Impairments by Propranolol in Humans. Biol Psychiatry 71: 380-386. https://doi.org/10.1016/j.biopsych.2011.10.028 ![]() |
[116] |
Cahill L, Pham CA, Setlow B (2000) Impaired Memory Consolidation in Rats Produced with β-Adrenergic Blockade. Neurobiol Learn Mem 74: 259-266. https://doi.org/10.1006/nlme.1999.3950 ![]() |
[117] |
Soeter M, Kindt M (2015) An Abrupt Transformation of Phobic Behavior After a Post-Retrieval Amnesic Agent. Biol Psychiatry 78: 880-886. https://doi.org/10.1016/j.biopsych.2015.04.006 ![]() |
[118] |
LaBar KS, Cabeza R (2006) Cognitive neuroscience of emotional memory. Nat Rev Neurosci 7: 54-64. https://doi.org/10.1038/nrn1825 ![]() |
[119] |
Liang KC, Juler RG, McGaugh JL (1986) Modulating effects of posttraining epinephrine on memory: Involvement of the amygdala noradrenergic system. Brain Res 368: 125-133. https://doi.org/10.1016/0006-8993(86)91049-8 ![]() |
[120] |
Dunsmoor JE, Niv Y, Daw N, et al. (2015) Rethinking Extinction. Neuron 88: 47-63. https://doi.org/10.1016/j.neuron.2015.09.028 ![]() |
[121] |
Blundell J, Kouser M, Powell CM (2008) Systemic inhibition of mammalian target of rapamycin inhibits fear memory reconsolidation. Neurobiol Learn Mem 90: 28-35. https://doi.org/10.1016/j.nlm.2007.12.004 ![]() |
[122] |
Galanopoulou AS, Buckmaster PS, Staley KJ, et al. (2012) Identification of new epilepsy treatments: Issues in preclinical methodology. Epilepsia 53: 571-582. https://doi.org/10.1111/j.1528-1167.2011.03391.x ![]() |
[123] |
González Otárula KA, von Ellenrieder N, Cuello-Oderiz C, et al. (2019) High-Frequency Oscillation Networks and Surgical Outcome in Adult Focal Epilepsy. Ann Neurol 85: 485-494. https://doi.org/10.1002/ana.25442 ![]() |
[124] |
Roullet P, Vaiva G, Véry E, et al. (2021) Traumatic memory reactivation with or without propranolol for PTSD and comorbid MD symptoms: a randomised clinical trial. Neuropsychopharmacology 46: 1643-1649. https://doi.org/10.1038/s41386-021-00984-w ![]() |
[125] |
Trenite DGAK-N, DiVentura BD, Pollard JR, et al. (2019) Suppression of the photoparoxysmal response in photosensitive epilepsy with cenobamate (YKP3089). Neurology 93: e559-e567. https://doi.org/10.1212/WNL.0000000000007894 ![]() |
[126] | Schjetnan AG, Luczak A (2011) Recording large-scale neuronal ensembles with silicon probes in the anesthetized rat. JoVE (Journal of Visualized Experiments) 19: e3282. https://doi.org/10.3791/3282 |
[127] |
Luczak A, Narayanan NS (2005) Spectral representation—analyzing single-unit activity in extracellularly recorded neuronal data without spike sorting. J Neurosci Meth 144: 53-61. https://doi.org/10.1016/j.jneumeth.2004.10.009 ![]() |
[128] |
Ryait H, Bermudez-Contreras E, Harvey M, et al. (2019) Data-driven analyses of motor impairments in animal models of neurological disorders. PLoS Biology 17: e3000516. https://doi.org/10.1371/journal.pbio.3000516 ![]() |
[129] |
Luczak A, McNaughton BL, Kubo Y (2022) Neurons learn by predicting future activity. Nat Mach Intell 4: 62-72. https://doi.org/10.1038/s42256-021-00430-y ![]() |
[130] | Chalmers E, Contreras EB, Robertson B, Luczak A, Gruber A (2017) Learning to predict consequences as a method of knowledge transfer in reinforcement learning. IEEE T Neural Network Learn Systems 29(6): 2259-2270. https://doi.org/10.1109/TNNLS.2017.2690910 |
1. | Aqeel Ahmad, Muhammad Farman, Ali Akgül, Nabila Bukhari, Sumaiyah Imtiaz, Mathematical analysis and numerical simulation of co-infection of TB-HIV, 2020, 27, 2576-5299, 431, 10.1080/25765299.2020.1840771 | |
2. | Rana Muhammad Zulqarnain, Imran Siddique, Fahd Jarad, Rifaqat Ali, Thabet Abdeljawad, Ahmed Mostafa Khalil, Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID-19 Pandemic, 2021, 2021, 1099-0526, 1, 10.1155/2021/6634991 | |
3. | Waheed Ahmad, Mujahid Abbas, Effect of quarantine on transmission dynamics of Ebola virus epidemic: a mathematical analysis, 2021, 136, 2190-5444, 10.1140/epjp/s13360-021-01360-9 | |
4. | Muhammad Farman, Aqeel Ahmad, Ali Akg黮, Muhammad Umer Saleem, Muhammad Naeem, Dumitru Baleanu, Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects, 2021, 67, 1546-2226, 3215, 10.32604/cmc.2021.014006 | |
5. | SHAHER MOMANI, R. P. CHAUHAN, SUNIL KUMAR, SAMIR HADID, A THEORETICAL STUDY ON FRACTIONAL EBOLA HEMORRHAGIC FEVER MODEL, 2022, 30, 0218-348X, 10.1142/S0218348X22400321 | |
6. | Maryam Amin, Muhammad Farman, Ali Akgül, Mohammad Partohaghighi, Fahd Jarad, Computational analysis of COVID-19 model outbreak with singular and nonlocal operator, 2022, 7, 2473-6988, 16741, 10.3934/math.2022919 | |
7. | Muhammad Farman, Ali Akg黮, Aqeel Ahmad, Dumitru Baleanu, Muhammad Umer Saleem, Dynamical Transmission of Coronavirus Model with Analysis and Simulation, 2021, 127, 1526-1506, 753, 10.32604/cmes.2021.014882 | |
8. | Jie Liu, Peng Zhang, Hailian Gui, Tong Xing, Hao Liu, Chen Zhang, Resonance study of fractional-order strongly nonlinear duffing systems, 2024, 98, 0973-1458, 3317, 10.1007/s12648-024-03080-z | |
9. | Isaac K. Adu, Fredrick A. Wireko, Mojeeb Al-R. El-N. Osman, Joshua Kiddy K. Asamoah, A fractional order Ebola transmission model for dogs and humans, 2024, 24, 24682276, e02230, 10.1016/j.sciaf.2024.e02230 | |
10. | Mohammed A. Almalahi, Khaled Aldowah, Faez Alqarni, Manel Hleili, Kamal Shah, Fathea M. O. Birkea, On modified Mittag–Leffler coupled hybrid fractional system constrained by Dhage hybrid fixed point in Banach algebra, 2024, 14, 2045-2322, 10.1038/s41598-024-81568-8 | |
11. | Kamel Guedri, Rahat Zarin, Mowffaq Oreijah, Samaher Khalaf Alharbi, Hamiden Abd El-Wahed Khalifa, Artificial neural network-driven modeling of Ebola transmission dynamics with delays and disability outcomes, 2025, 115, 14769271, 108350, 10.1016/j.compbiolchem.2025.108350 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.5 |
1 | 39.6912 | 39.5848 | 39.51 | 39.4383 |
1.5 | 39.3299 | 39.1117 | 39.0235 | 39.1181 |
3 | 37.2519 | 36.2268 | 36.264 | 37.5584 |
4.5 | 32.0652 | 29.2568 | 30.0105 | 34.514 |
6 | 19.0984 | 14.0068 | 17.2162 | 29.3074 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
1 | 10.4879 | 10.6026 | 10.6542 | 10.7698 |
2 | 12.052 | 11.9378 | 11.8579 | 11.5689 |
4 | 13.2768 | 12.5387 | 12.2499 | 11.8581 |
6 | 8.7256 | 9.97166 | 10.5704 | 12.7973 |
8 | 5.0464 | 11.4457 | 13.7013 | 19.4353 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
2 | 20.504 | 20.5195 | 20.5331 | 20.5414 |
4 | 21.952 | 21.8288 | 21.6815 | 21.509 |
6 | 25.448 | 24.6081 | 23.8154 | 23.076 |
8 | 32.096 | 29.4003 | 27.1489 | 25.2921 |
10 | 43 | 36.6889 | 31.8489 | 28.1877 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
0.5 | 10.5931 | 10.6768 | 10.7803 | 10.9131 |
1 | 11.3486 | 11.5116 | 11.7127 | 11.9551 |
1.5 | 12.531 | 12.8083 | 13.1141 | 13.4308 |
2 | 14.4048 | 14.7773 | 15.124 | 15.4064 |
t | ϕ = 1 | ϕ = 0.95 | ϕ = 0.9 | ϕ = 0.85 |
1 | 5.67835 | 5.6959 | 5.68235 | 5.7302 |
2 | 6.4746 | 6.46707 | 6.45834 | 6.44629 |
4 | 8.788 | 8.62982 | 8.47227 | 8.30553 |
6 | 12.6746 | 12.1038 | 11.562 | 11.0225 |
8 | 18.8688 | 17.417 | 16.0958 | 14.8435 |
10 | 28.105 | 25.0658 | 22.3972 | 19.9683 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.5 |
1 | 39.6912 | 39.5848 | 39.51 | 39.4383 |
1.5 | 39.3299 | 39.1117 | 39.0235 | 39.1181 |
3 | 37.2519 | 36.2268 | 36.264 | 37.5584 |
4.5 | 32.0652 | 29.2568 | 30.0105 | 34.514 |
6 | 19.0984 | 14.0068 | 17.2162 | 29.3074 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
1 | 10.4879 | 10.6026 | 10.6542 | 10.7698 |
2 | 12.052 | 11.9378 | 11.8579 | 11.5689 |
4 | 13.2768 | 12.5387 | 12.2499 | 11.8581 |
6 | 8.7256 | 9.97166 | 10.5704 | 12.7973 |
8 | 5.0464 | 11.4457 | 13.7013 | 19.4353 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
2 | 20.504 | 20.5195 | 20.5331 | 20.5414 |
4 | 21.952 | 21.8288 | 21.6815 | 21.509 |
6 | 25.448 | 24.6081 | 23.8154 | 23.076 |
8 | 32.096 | 29.4003 | 27.1489 | 25.2921 |
10 | 43 | 36.6889 | 31.8489 | 28.1877 |
t | ϕ = 1 | ϕ = 0.9 | ϕ = 0.8 | ϕ = 0.7 |
0.5 | 10.5931 | 10.6768 | 10.7803 | 10.9131 |
1 | 11.3486 | 11.5116 | 11.7127 | 11.9551 |
1.5 | 12.531 | 12.8083 | 13.1141 | 13.4308 |
2 | 14.4048 | 14.7773 | 15.124 | 15.4064 |
t | ϕ = 1 | ϕ = 0.95 | ϕ = 0.9 | ϕ = 0.85 |
1 | 5.67835 | 5.6959 | 5.68235 | 5.7302 |
2 | 6.4746 | 6.46707 | 6.45834 | 6.44629 |
4 | 8.788 | 8.62982 | 8.47227 | 8.30553 |
6 | 12.6746 | 12.1038 | 11.562 | 11.0225 |
8 | 18.8688 | 17.417 | 16.0958 | 14.8435 |
10 | 28.105 | 25.0658 | 22.3972 | 19.9683 |