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Mathematical Biosciences and Engineering, 2019, 16(3): 1313-1333. doi: 10.3934/mbe.2019064
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Sex-structured wild and sterile mosquito population models with different release strategies
1 School of Information Science and Technology, Donghua University, Shanghai 201620, China
2 School of Science, Donghua University, Shanghai 201620, China
3 Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 2Y2, Canada
4 Center for Applied Mathematics, Guangzhou University, Guangzhou, 510320, China
5 Department of Mathematical Sciences, The University of Alabama in Huntsville, Huntsville, AL 35899, USA
Received: , Accepted: , Published:
Special Issues: Mathematical Modeling of Mosquito-Borne Diseases
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Mathematical Biosciences and Engineering,2014, 11(3): 203-215.doi: 10.3934/mbe.2014.11.203
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Stability and optimal control for some classes of tritrophic systems
Luca Galbusera, Sara Pasquali, Gianni Gilioli
Mathematical Biosciences and Engineering,2014, 11(3): 257-283.doi: 10.3934/mbe.2014.11.257
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Dynamics of an age-of-infection cholera model
Fred Brauer, Zhisheng Shuai, P. van den Driessche
Mathematical Biosciences and Engineering,2013, 10(3): 1335-1349.doi: 10.3934/mbe.2013.10.1335
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Chemostats and epidemics: Competition for nutrients/hosts
Hal L. Smith, Horst R. Thieme
Mathematical Biosciences and Engineering,2013, 10(3): 1635-1650.doi: 10.3934/mbe.2013.10.1635
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Model for hepatitis C virus transmissions
Elamin H. Elbasha
Mathematical Biosciences and Engineering,2013, 10(3): 1045-1065.doi: 10.3934/mbe.2013.10.1045
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Maya Mincheva, Gheorghe Craciun
Mathematical Biosciences and Engineering,2013, 10(3): 1207-1226.doi: 10.3934/mbe.2013.10.1207
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The ratio of hidden HIV infection in Cuba
Miguel Atencia, Esther García-Garaluz, Gonzalo Joya
Mathematical Biosciences and Engineering,2013, 10(3): 959-977.doi: 10.3934/mbe.2013.10.959
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Gompertz model with delays and treatment: Mathematical analysis
Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś
Mathematical Biosciences and Engineering,2013, 10(3): 551-563.doi: 10.3934/mbe.2013.10.551
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On the sensitivity of feature ranked lists for large-scale biological data
Danuta Gaweł, Krzysztof Fujarewicz
Mathematical Biosciences and Engineering,2013, 10(3): 667-690.doi: 10.3934/mbe.2013.10.667
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A simple model of carcinogenic mutations with time delay and diffusion
Monika Joanna Piotrowska, Urszula Foryś, Marek Bodnar, Jan Poleszczuk
Mathematical Biosciences and Engineering,2013, 10(3): 861-872.doi: 10.3934/mbe.2013.10.861
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Eduardo González-Olivares, Betsabé González-Yañez, Jaime Mena-Lorca, José D. Flores
Mathematical Biosciences and Engineering,2013, 10(3): 345-367.doi: 10.3934/mbe.2013.10.345
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Lyapunov functions and global stability for SIR and SEIR models withage-dependent susceptibility
Andrey V. Melnik, Andrei Korobeinikov
Mathematical Biosciences and Engineering,2013, 10(3): 369-378.doi: 10.3934/mbe.2013.10.369
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Mathematical modelling and control of echinococcus in Qinghai province, China
Liumei Wu, Baojun Song, Wen Du, Jie Lou
Mathematical Biosciences and Engineering,2013, 10(3): 425-444.doi: 10.3934/mbe.2013.10.425
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On latencies in malaria infections and their impact on the disease dynamics
Yanyu Xiao, Xingfu Zou
Mathematical Biosciences and Engineering,2013, 10(3): 463-481.doi: 10.3934/mbe.2013.10.463
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Zhaohui Yuan, Xingfu Zou
Mathematical Biosciences and Engineering,2013, 10(3): 483-498.doi: 10.3934/mbe.2013.10.483
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Model of tumour angiogenesis -- analysis of stability with respect to delays
Marek Bodnar, Monika Joanna Piotrowska, Urszula Foryś, Ewa Nizińska
Mathematical Biosciences and Engineering,2013, 10(3): 19-35.doi: 10.3934/mbe.2013.10.19
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On a mathematical model of tumor growth based on cancer stem cells
J. Ignacio Tello
Mathematical Biosciences and Engineering,2013, 10(3): 263-278.doi: 10.3934/mbe.2013.10.263
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C. Connell McCluskey
Mathematical Biosciences and Engineering,2012, 9(3): 819-841.doi: 10.3934/mbe.2012.9.819
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Modeling the effects of introducing a new antibiotic in a hospital setting: A case study
Michele L. Joyner, Cammey C. Manning, Brandi N. Canter
Mathematical Biosciences and Engineering,2012, 9(3): 601-625.doi: 10.3934/mbe.2012.9.601
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The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat
Tewfik Sari, Miled El Hajji, Jérôme Harmand
Mathematical Biosciences and Engineering,2012, 9(3): 627-645.doi: 10.3934/mbe.2012.9.627
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A minimal mathematical model for the initial molecular interactions of death receptor signalling
Christian Winkel, Simon Neumann, Christina Surulescu, Peter Scheurich
Mathematical Biosciences and Engineering,2012, 9(3): 663-683.doi: 10.3934/mbe.2012.9.663
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Global stability for epidemic model with constant latency and infectious periods
Gang Huang, Edoardo Beretta, Yasuhiro Takeuchi
Mathematical Biosciences and Engineering,2012, 9(3): 297-312.doi: 10.3934/mbe.2012.9.297
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Impact of heterogeneity on the dynamics of an SEIR epidemic model
Zhisheng Shuai, P. van den Driessche
Mathematical Biosciences and Engineering,2012, 9(3): 393-411.doi: 10.3934/mbe.2012.9.393
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Analysis of a model for the effects of an external toxin on anaerobic digestion
Marion Weedermann
Mathematical Biosciences and Engineering,2012, 9(3): 445-459.doi: 10.3934/mbe.2012.9.445
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Threshold dynamics for a Tuberculosis model with seasonality
Xinli Hu
Mathematical Biosciences and Engineering,2012, 9(3): 111-122.doi: 10.3934/mbe.2012.9.111
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Cruz Vargas-De-León
Mathematical Biosciences and Engineering,2012, 9(3): 165-174.doi: 10.3934/mbe.2012.9.165
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Impact of discontinuous treatments on disease dynamics in an SIR epidemic model
Zhenyuan Guo, Lihong Huang, Xingfu Zou
Mathematical Biosciences and Engineering,2012, 9(3): 97-110.doi: 10.3934/mbe.2012.9.97
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Andrey V. Melnik, Andrei Korobeinikov
Mathematical Biosciences and Engineering,2011, 8(3): 1019-1034.doi: 10.3934/mbe.2011.8.1019
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Dynamics of a delay Schistosomiasis model in snail infections
Chunhua Shan, Hongjun Gao, Huaiping Zhu
Mathematical Biosciences and Engineering,2011, 8(3): 1099-1115.doi: 10.3934/mbe.2011.8.1099
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A dynamic model describing heterotrophic culture of chorella and its stability analysis
Yan Zhang, Wanbiao Ma, Hai Yan, Yasuhiro Takeuchi
Mathematical Biosciences and Engineering,2011, 8(3): 1117-1133.doi: 10.3934/mbe.2011.8.1117
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Zhenzhen Zheng, Ching-Shan Chou, Tau-Mu Yi, Qing Nie
Mathematical Biosciences and Engineering,2011, 8(3): 1135-1168.doi: 10.3934/mbe.2011.8.1135
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An SEIR epidemic model with constant latency time and infectious period
Edoardo Beretta, Dimitri Breda
Mathematical Biosciences and Engineering,2011, 8(3): 931-952.doi: 10.3934/mbe.2011.8.931
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Effects of spatial structure and diffusion on the performances of the chemostat
Ihab Haidar, Alain Rapaport, Frédéric Gérard
Mathematical Biosciences and Engineering,2011, 8(3): 953-971.doi: 10.3934/mbe.2011.8.953
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A note for the global stability of a delay differential equation of hepatitis B virus infection
Bao-Zhu Guo, Li-Ming Cai
Mathematical Biosciences and Engineering,2011, 8(3): 689-694.doi: 10.3934/mbe.2011.8.689
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Hongbin Guo, Jianhong Wu
Mathematical Biosciences and Engineering,2011, 8(3): 695-709.doi: 10.3934/mbe.2011.8.695
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Modeling the effects of carriers on transmission dynamics of infectious diseases
Darja Kalajdzievska, Michael Yi Li
Mathematical Biosciences and Engineering,2011, 8(3): 711-722.doi: 10.3934/mbe.2011.8.711
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Stability analysis and application of a mathematical cholera model
Shu Liao, Jin Wang
Mathematical Biosciences and Engineering,2011, 8(3): 733-752.doi: 10.3934/mbe.2011.8.733
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Optimal number of sites in multi-site fisheries with fish stock dependent migrations
Ali Moussaoui, Pierre Auger, Christophe Lett
Mathematical Biosciences and Engineering,2011, 8(3): 769-783.doi: 10.3934/mbe.2011.8.769
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Global dynamics of the chemostat with different removal rates and variable yields
Tewfik Sari, Frederic Mazenc
Mathematical Biosciences and Engineering,2011, 8(3): 827-840.doi: 10.3934/mbe.2011.8.827
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Sveir epidemiological model with varying infectivity and distributed delays
Jinliang Wang, Gang Huang, Yasuhiro Takeuchi, Shengqiang Liu
Mathematical Biosciences and Engineering,2011, 8(3): 875-888.doi: 10.3934/mbe.2011.8.875
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Blood coagulation dynamics: mathematical modeling and stability results
Adélia Sequeira, Rafael F. Santos, Tomáš Bodnár
Mathematical Biosciences and Engineering,2011, 8(3): 425-443.doi: 10.3934/mbe.2011.8.425
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Orit Lavi, Doron Ginsberg, Yoram Louzoun
Mathematical Biosciences and Engineering,2011, 8(3): 445-461.doi: 10.3934/mbe.2011.8.445
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Physiologically structured populations with diffusion and dynamic boundary conditions
József Z. Farkas, Peter Hinow
Mathematical Biosciences and Engineering,2011, 8(3): 503-513.doi: 10.3934/mbe.2011.8.503
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A delay-differential equation model of HIV related cancer--immune system dynamics
Urszula Foryś, Jan Poleszczuk
Mathematical Biosciences and Engineering,2011, 8(3): 627-641.doi: 10.3934/mbe.2011.8.627
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Stability of a delay equation arising from a juvenile-adult model
Azmy S. Ackleh, Keng Deng
Mathematical Biosciences and Engineering,2010, 7(3): 729-737.doi: 10.3934/mbe.2010.7.729
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A stoichiometrically derived algal growth model and its global analysis
Xiong Li, Hao Wang
Mathematical Biosciences and Engineering,2010, 7(3): 825-836.doi: 10.3934/mbe.2010.7.825
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Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence
C. Connell McCluskey
Mathematical Biosciences and Engineering,2010, 7(3): 837-850.doi: 10.3934/mbe.2010.7.837
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Robert Artebrant, Aslak Tveito, Glenn T. Lines
Mathematical Biosciences and Engineering,2010, 7(3): 505-526.doi: 10.3934/mbe.2010.7.505
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Bruno Buonomo, Alberto d’Onofrio, Deborah Lacitignola
Mathematical Biosciences and Engineering,2010, 7(3): 561-578.doi: 10.3934/mbe.2010.7.561
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Local stabilization and network synchronization: The case of stationary regimes
Stefano Fasani, Sergio Rinaldi
Mathematical Biosciences and Engineering,2010, 7(3): 623-639.doi: 10.3934/mbe.2010.7.623
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A mathematical study of a syntrophic relationship of a model of anaerobic digestion process
Miled El Hajji, Frédéric Mazenc, Jérôme Harmand
Mathematical Biosciences and Engineering,2010, 7(3): 641-656.doi: 10.3934/mbe.2010.7.641
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Global stability of an HIV-1 model with distributed intracellular delays and a combination therapy
Shengqiang Liu, Lin Wang
Mathematical Biosciences and Engineering,2010, 7(3): 675-685.doi: 10.3934/mbe.2010.7.675
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Morphological spatial patterns in a reaction diffusion model for metal growth
Benedetto Bozzini, Deborah Lacitignola, Ivonne Sgura
Mathematical Biosciences and Engineering,2010, 7(3): 237-258.doi: 10.3934/mbe.2010.7.237
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Surface tension and modeling of cellular intercalation during zebrafish gastrulation
Colette Calmelet, Diane Sepich
Mathematical Biosciences and Engineering,2010, 7(3): 259-275.doi: 10.3934/mbe.2010.7.259
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Vector control for the Chikungunya disease
Yves Dumont, Frederic Chiroleu
Mathematical Biosciences and Engineering,2010, 7(3): 313-345.doi: 10.3934/mbe.2010.7.313
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Global stability for a class of discrete SIR epidemic models
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya
Mathematical Biosciences and Engineering,2010, 7(3): 347-361.doi: 10.3934/mbe.2010.7.347
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An age-structured two-strain epidemic model with super-infection
Xue-Zhi Li, Ji-Xuan Liu, Maia Martcheva
Mathematical Biosciences and Engineering,2010, 7(3): 123-147.doi: 10.3934/mbe.2010.7.123
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Dynamics of an SIS reaction-diffusion epidemic model for disease transmission
Wenzhang Huang, Maoan Han, Kaiyu Liu
Mathematical Biosciences and Engineering,2010, 7(3): 51-66.doi: 10.3934/mbe.2010.7.51
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Discrete host-parasitoid models with Allee effects and age structure in the host
Sophia R.-J. Jang
Mathematical Biosciences and Engineering,2010, 7(3): 67-81.doi: 10.3934/mbe.2010.7.67
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Multistability, oscillations and bifurcations in feedback loops
Maria Conceição A. Leite, Yunjiao Wang
Mathematical Biosciences and Engineering,2010, 7(3): 83-97.doi: 10.3934/mbe.2010.7.83
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Modeling of mosquitoes with dominant or recessive Transgenes and Allee effects
Jia Li
Mathematical Biosciences and Engineering,2010, 7(3): 99-121.doi: 10.3934/mbe.2010.7.99
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Stability of equilibria of a predator-prey model of phenotype evolution
Sílvia Cuadrado
Mathematical Biosciences and Engineering,2009, 6(3): 701-718.doi: 10.3934/mbe.2009.6.701
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Sharpness of saturation in harvesting and predation
Christopher M. Kribs-Zaleta
Mathematical Biosciences and Engineering,2009, 6(3): 719-742.doi: 10.3934/mbe.2009.6.719
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Novel stability results for traveling wavefronts in an age-structured reaction-diffusion equation
Ming Mei, Yau Shu Wong
Mathematical Biosciences and Engineering,2009, 6(3): 743-752.doi: 10.3934/mbe.2009.6.743
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Esther Chigidi, Edward M. Lungu
Mathematical Biosciences and Engineering,2009, 6(3): 427-450.doi: 10.3934/mbe.2009.6.427
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Global asymptotic properties for a Leslie-Gower food chain model
Andrei Korobeinikov, William T. Lee
Mathematical Biosciences and Engineering,2009, 6(3): 585-590.doi: 10.3934/mbe.2009.6.585
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Global stability for an SEIR epidemiological model with varying infectivity and infinite delay
C. Connell McCluskey
Mathematical Biosciences and Engineering,2009, 6(3): 603-610.doi: 10.3934/mbe.2009.6.603
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Feedback stabilization for a chemostat with delayed output
Gonzalo Robledo
Mathematical Biosciences and Engineering,2009, 6(3): 629-647.doi: 10.3934/mbe.2009.6.629
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Epidemic models with differential susceptibility and staged progression and their dynamics
James M. Hyman, Jia Li
Mathematical Biosciences and Engineering,2009, 6(3): 321-332.doi: 10.3934/mbe.2009.6.321
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Mathematical analysis of a model for HIV-malaria co-infection
Zindoga Mukandavire, Abba B. Gumel, Winston Garira, Jean Michel Tchuenche
Mathematical Biosciences and Engineering,2009, 6(3): 333-362.doi: 10.3934/mbe.2009.6.333
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Muntaser Safan, Klaus Dietz
Mathematical Biosciences and Engineering,2009, 6(3): 395-407.doi: 10.3934/mbe.2009.6.395
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Global stability of a class of discrete age-structured SIS models with immigration
Yicang Zhou, Zhien Ma
Mathematical Biosciences and Engineering,2009, 6(3): 409-425.doi: 10.3934/mbe.2009.6.409
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Feedback regulation in multistage cell lineages
Wing-Cheong Lo, Ching-Shan Chou, Kimberly K. Gokoffski, Frederic Y.-M. Wan, Arthur D. Lander, Anne L. Calof, Qing Nie
Mathematical Biosciences and Engineering,2009, 6(3): 59-82.doi: 10.3934/mbe.2009.6.59
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Mathematical analysis of a HIV model with frequency dependence and viral diversity
Shingo Iwami, Shinji Nakaoka, Yasuhiro Takeuchi
Mathematical Biosciences and Engineering,2008, 5(3): 457-476.doi: 10.3934/mbe.2008.5.457
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Stabilization due to predator interference: comparison of different analysis approaches
G.A.K. van Voorn, D. Stiefs, T. Gross, B. W. Kooi, Ulrike Feudel, S.A.L.M. Kooijman
Mathematical Biosciences and Engineering,2008, 5(3): 567-583.doi: 10.3934/mbe.2008.5.567
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SEIR epidemiological model with varying infectivity and infinite delay
Gergely Röst, Jianhong Wu
Mathematical Biosciences and Engineering,2008, 5(3): 389-402.doi: 10.3934/mbe.2008.5.389
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Modeling and prediction of HIV in China: transmission rates structured by infection ages
Yicang Zhou, Yiming Shao, Yuhua Ruan, Jianqing Xu, Zhien Ma, Changlin Mei, Jianhong Wu
Mathematical Biosciences and Engineering,2008, 5(3): 403-418.doi: 10.3934/mbe.2008.5.403
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A passivity-based stability criterion for a class of biochemical reaction networks
Murat Arcak, Eduardo D. Sontag
Mathematical Biosciences and Engineering,2008, 5(3): 1-19.doi: 10.3934/mbe.2008.5.1
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Oluwaseun Sharomi, Chandra N. Podder, Abba B. Gumel, Baojun Song
Mathematical Biosciences and Engineering,2008, 5(3): 145-174.doi: 10.3934/mbe.2008.5.145
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Global stability analysis for SEIS models with n latent classes
Napoleon Bame, Samuel Bowong, Josepha Mbang, Gauthier Sallet, Jean-Jules Tewa
Mathematical Biosciences and Engineering,2008, 5(3): 20-33.doi: 10.3934/mbe.2008.5.20
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A storage model with random release rate for modeling exposure to food contaminants
Patrice Bertail, Stéphan Clémençon, Jessica Tressou
Mathematical Biosciences and Engineering,2008, 5(3): 35-60.doi: 10.3934/mbe.2008.5.35
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Nonlinear stability of traveling wavefronts in an age-structured reaction-diffusion population model
Guangrui Li, Ming Mei, Yau Shu Wong
Mathematical Biosciences and Engineering,2008, 5(3): 85-100.doi: 10.3934/mbe.2008.5.85
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Global stability of equilibria in a tick-borne disease model
Shangbing Ai
Mathematical Biosciences and Engineering,2007, 4(3): 567-572.doi: 10.3934/mbe.2007.4.567
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Global analysis of discrete-time SI and SIS epidemic models
Jianquan Li, Zhien Ma, Fred Brauer
Mathematical Biosciences and Engineering,2007, 4(3): 699-710.doi: 10.3934/mbe.2007.4.699
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Effects of predation efficiencies on the dynamics of a tritrophic food chain
Maria Paola Cassinari, Maria Groppi, Claudio Tebaldi
Mathematical Biosciences and Engineering,2007, 4(3): 431-456.doi: 10.3934/mbe.2007.4.431
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Modeling diseases with latency and relapse
P. van den Driessche, Lin Wang, Xingfu Zou
Mathematical Biosciences and Engineering,2007, 4(3): 205-219.doi: 10.3934/mbe.2007.4.205
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Subthreshold coexistence of strains: the impact of vaccination and mutation
Maia Martcheva, Mimmo Iannelli, Xue-Zhi Li
Mathematical Biosciences and Engineering,2007, 4(3): 287-317.doi: 10.3934/mbe.2007.4.287
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On the stability of periodic solutions in the perturbed chemostat
Frédéric Mazenc, Michael Malisoff, Patrick D. Leenheer
Mathematical Biosciences and Engineering,2007, 4(3): 319-338.doi: 10.3934/mbe.2007.4.319
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The stability of stationary fronts for a discrete nerve axon model
Christopher E. Elmer
Mathematical Biosciences and Engineering,2007, 4(3): 113-129.doi: 10.3934/mbe.2007.4.113
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Lyapunov functions for tuberculosis models with fast and slow progression
C. Connell Mccluskey
Mathematical Biosciences and Engineering,2006, 3(3): 603-614.doi: 10.3934/mbe.2006.3.603
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Stochastic epidemic models with a backward bifurcation
Linda J. S. Allen, P. van den Driessche
Mathematical Biosciences and Engineering,2006, 3(3): 445-458.doi: 10.3934/mbe.2006.3.445
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Competition and Dispersal Delays in Patchy Environments
Nancy Azer, P. van den Driessche
Mathematical Biosciences and Engineering,2006, 3(3): 283-296.doi: 10.3934/mbe.2006.3.283
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Modeling Cancer in HIV-1 Infected Individuals: Equilibria, Cycles and Chaotic Behavior
Jie Lou, Tommaso Ruggeri, Claudio Tebaldi
Mathematical Biosciences and Engineering,2006, 3(3): 313-324.doi: 10.3934/mbe.2006.3.313
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Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model
Fabien Crauste
Mathematical Biosciences and Engineering,2006, 3(3): 325-346.doi: 10.3934/mbe.2006.3.325
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Energy Considerations in a Model of Nematode Sperm Crawling
Borys V. Bazaliy, Ya. B. Bazaliy, Avner Friedman, Bei Hu
Mathematical Biosciences and Engineering,2006, 3(3): 347-370.doi: 10.3934/mbe.2006.3.347
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The stability of an SIR epidemic model with time delays
Zhen Jin, Zhien Ma
Mathematical Biosciences and Engineering,2006, 3(3): 101-109.doi: 10.3934/mbe.2006.3.101
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A competition model of the chemostat with an external inhibitor
Jianquan Li, Zuren Feng, Juan Zhang, Jie Lou
Mathematical Biosciences and Engineering,2006, 3(3): 111-123.doi: 10.3934/mbe.2006.3.111
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Nonlinear semelparous Leslie models
J. M. Cushing
Mathematical Biosciences and Engineering,2006, 3(3): 17-36.doi: 10.3934/mbe.2006.3.17
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A nonlinear $L^2$-stability analysis for two-species population dynamics with dispersal
Salvatore Rionero
Mathematical Biosciences and Engineering,2006, 3(3): 189-204.doi: 10.3934/mbe.2006.3.189
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An improved model of t cell development in the thymus and its stability analysis
Hongjing Shi, Wanbiao Ma
Mathematical Biosciences and Engineering,2006, 3(3): 237-248.doi: 10.3934/mbe.2006.3.237
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Epidemic models with nonlinear infection forces
Wendi Wang
Mathematical Biosciences and Engineering,2006, 3(3): 267-279.doi: 10.3934/mbe.2006.3.267
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An allelopathic competition model with quorum sensing and delayed toxicant production
Paolo Fergola, Marianna Cerasuolo, Edoardo Beretta
Mathematical Biosciences and Engineering,2006, 3(3): 37-50.doi: 10.3934/mbe.2006.3.37
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Some bifurcation methods of finding limit cycles
Maoan Han, Tonghua Zhang
Mathematical Biosciences and Engineering,2006, 3(3): 67-77.doi: 10.3934/mbe.2006.3.67
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Differential susceptibility and infectivity epidemic models
James M. Hyman, Jia Li
Mathematical Biosciences and Engineering,2006, 3(3): 89-100.doi: 10.3934/mbe.2006.3.89
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Host Extinction Dynamics in a Simple Parasite-Host Interaction Model
Tzy-Wei Hwang, Yang Kuang
Mathematical Biosciences and Engineering,2005, 2(3): 743-751.doi: 10.3934/mbe.2005.2.743
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Time Delay In Necrotic Core Formation
Marek Bodnar, Urszula Foryś
Mathematical Biosciences and Engineering,2005, 2(3): 461-472.doi: 10.3934/mbe.2005.2.461
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Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models
Urszula Foryś, Yuri Kheifetz, Yuri Kogan
Mathematical Biosciences and Engineering,2005, 2(3): 511-525.doi: 10.3934/mbe.2005.2.511
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Spatially Distributed Morphogen Production and Morphogen Gradient Formation
Arthur D. Lander, Qing Nie, Frederic Y. M. Wan
Mathematical Biosciences and Engineering,2005, 2(3): 239-262.doi: 10.3934/mbe.2005.2.239
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Two-Species Competition with High Dispersal: The Winning Strategy
S.A. Gourley, Yang Kuang
Mathematical Biosciences and Engineering,2005, 2(3): 345-362.doi: 10.3934/mbe.2005.2.345
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A Simple Epidemic Model with Surprising Dynamics
F. Berezovskaya, G. Karev, Baojun Song, Carlos Castillo-Chavez
Mathematical Biosciences and Engineering,2005, 2(3): 133-152.doi: 10.3934/mbe.2005.2.133
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On Predator-Prey Systems and Small-Gain Theorems
Patrick D. Leenheer, David Angeli, Eduardo D. Sontag
Mathematical Biosciences and Engineering,2005, 2(3): 25-42.doi: 10.3934/mbe.2005.2.25
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Turing instabilities and pattern formation in a benthic nutrient-microorganism system
Martin Baurmann, Wolfgang Ebenhöh, Ulrike Feudel
Mathematical Biosciences and Engineering,2004, 1(3): 111-130.doi: 10.3934/mbe.2004.1.111
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Andrei Korobeinikov, Philip K. Maini
Mathematical Biosciences and Engineering,2004, 1(3): 57-60.doi: 10.3934/mbe.2004.1.57
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Complexity, big data and financial stability
Charilaos Mertzanis
Quantitative Finance and Economics,2018, 2(3): 637-660.doi: 10.3934/QFE.2018.3.637
Abstract + HTML + PDF(507 KB)
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Zeid Al Qaisi, Qais Alsafasfeh, Ahmad Harb
AIMS Energy,2018, 6(3): 832-845.doi: 10.3934/energy.2018.5.832
Abstract + HTML + PDF(1240 KB)
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Viktorija Dičpinigaitienė, Lina Novickytė
Quantitative Finance and Economics,2018, 2(3): 798-820.doi: 10.3934/QFE.2018.4.798
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Dynamics analysis of stochastic tuberculosis model transmission withimmune response
Jean Luc Dimi, Texance Mbaya
AIMS Mathematics,2018, 3(3): 391-408.doi: 10.3934/Math.2018.3.391
Abstract + HTML + PDF(251 KB)
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Dynamical analysis for a hepatitis B transmission model with immigration and infection age
Suxia Zhang, Hongbin Guo, Robert Smith?
Mathematical Biosciences and Engineering,2018, 15(3): 1291-1313.doi: 10.3934/mbe.2018060
Abstract + HTML + PDF(436 KB)
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A cholera mathematical model with vaccination and the biggest outbreak of world’s history
Ana P. Lemos-Paião, Cristiana J. Silva, Delfim F. M. Torres
AIMS Mathematics,2018, 3(3): 448-463.doi: 10.3934/Math.2018.4.448
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Modeling the control of infectious diseases: Effects of TV and social media advertisements
Arvind Kumar Misra, Rajanish Kumar Rai, Yasuhiro Takeuchi
Mathematical Biosciences and Engineering,2018, 15(3): 1315-1343.doi: 10.3934/mbe.2018061
Abstract + HTML + PDF(1627 KB)
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Feng Rao, Carlos Castillo-Chavez, Yun Kang
Mathematical Biosciences and Engineering,2018, 15(3): 1401-1423.doi: 10.3934/mbe.2018064
Abstract + HTML + PDF(1231 KB)
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Review of stability and stabilization for impulsive delayed systems
Xueyan Yang, Xiaodi Li, Qiang Xi, Peiyong Duan
Mathematical Biosciences and Engineering,2018, 15(3): 1495-1515.doi: 10.3934/mbe.2018069
Abstract + HTML + PDF(2010 KB)
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Smoking dynamics with health education effect
Pengcheng Xiao, Zeyu Zhang, Xianbo Sun
AIMS Mathematics,2018, 3(3): 584-599.doi: 10.3934/Math.2018.4.584
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Dynamics of a delay turbidostat system with contois growth rate
Yong Yao
Mathematical Biosciences and Engineering,2019, 16(3): 56-77.doi: 10.3934/mbe.2019003
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Population dynamic consequences of fearful prey in a spatiotemporal predator-prey system
Ranjit Kumar Upadhyay, Swati Mishra
Mathematical Biosciences and Engineering,2019, 16(3): 338-372.doi: 10.3934/mbe.2019017
Abstract + HTML + PDF(9537 KB)
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Alexis Erich S. Almocera, Sze-Bi Hsu, Polly W. Sy
Mathematical Biosciences and Engineering,2019, 16(3): 516-537.doi: 10.3934/mbe.2019024
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Yipeng Yang
AIMS Electronics and Electrical Engineering,2019, 3(3): 16-32.doi: 10.3934/ElectrEng.2019.1.16
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Yang Li, Jia Li
Mathematical Biosciences and Engineering,2019, 16(3): 572-602.doi: 10.3934/mbe.2019028
Abstract + HTML + PDF(810 KB)
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Modeling the impact of sanitation and awareness on the spread of infectious diseases
Rajanish Kumar Rai, Arvind Kumar Misra, Yasuhiro Takeuchi
Mathematical Biosciences and Engineering,2019, 16(3): 667-700.doi: 10.3934/mbe.2019032
Abstract + HTML + PDF(1585 KB)
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Traveling wave solutions to a neural field model with oscillatory synaptic coupling types
Alan Dyson
Mathematical Biosciences and Engineering,2019, 16(3): 727-758.doi: 10.3934/mbe.2019035
Abstract + HTML + PDF(1085 KB)
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Mathematical modeling the dynamics of Clonorchiasis in Guangzhou City of China
Ruixia Yuan, Shujing Gao, Jicai Huang, Xinan Zhang
Mathematical Biosciences and Engineering,2019, 16(3): 881-897.doi: 10.3934/mbe.2019041
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Modeling the imported malaria to north Africa and the absorption effect of the immigrants
Souâd Yacheur, Ali Moussaoui, Abdessamad Tridane
Mathematical Biosciences and Engineering,2019, 16(3): 967-989.doi: 10.3934/mbe.2019045
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Remarks on a variant of Lyapunov-LaSalle theorem
Songbai Guo, Wanbiao Ma
Mathematical Biosciences and Engineering,2019, 16(3): 1056-1066.doi: 10.3934/mbe.2019050
Abstract + HTML + PDF(659 KB)
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The dynamics of Zika virus with Caputo fractional derivative
Muhammad Altaf Khan, Saif Ullah, Muhammad Farhan
AIMS Mathematics,2019, 4(3): 134-146.doi: 10.3934/Math.2019.1.134
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Stability properties of neural networks with non-instantaneous impulses
Ravi Agarwal, Snezhana Hristova, Donal O’Regan, Radoslava Terzieva
Mathematical Biosciences and Engineering,2019, 16(3): 1210-1227.doi: 10.3934/mbe.2019058
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Analysis of spontaneous emergence of cell polarity with delayed negative feedback
Yue Liu,Wing-Cheong Lo
Mathematical Biosciences and Engineering,2019, 16(3): 1392-1413.doi: 10.3934/mbe.2019068
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Ann Nwankwo, Daniel Okuonghae
Mathematical Biosciences and Engineering,2019, 16(3): 1414-1444.doi: 10.3934/mbe.2019069
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Molecular dynamics study of mechanical properties of HMX–PS interface
Zhimin Cao, Chenhui Xu, Caiwei Xiao, Wei Liu, Jiaohu Huang, Wenjun Zong, Junjie Zhang, Tao Sun
AIMS Materials Science,2019, 6(3): 111-118.doi: 10.3934/matersci.2019.1.111
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A diffusive predator-prey system with prey refuge and predator cannibalism
Yuxuan Zhang, Xinmiao Rong, Jimin Zhang
Mathematical Biosciences and Engineering,2019, 16(3): 1445-1470.doi: 10.3934/mbe.2019070
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Global stability of an age-structured epidemic model with general Lyapunov functional
Abdennasser Chekroun, Mohammed Nor Frioui, Toshikazu Kuniya, Tarik Mohammed Touaoula
Mathematical Biosciences and Engineering,2019, 16(3): 1525-1553.doi: 10.3934/mbe.2019073
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Optimal harvesting of a competitive n-species stochastic model with delayed diffusions
Fangfang Zhu, Xinzhu Meng, Tonghua Zhang
Mathematical Biosciences and Engineering,2019, 16(3): 1554-1574.doi: 10.3934/mbe.2019074
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Global dynamics of an age-structured malaria model with prevention
Zhong-Kai Guo, Hai-Feng Huo, Hong Xiang
Mathematical Biosciences and Engineering,2019, 16(3): 1625-1653.doi: 10.3934/mbe.2019078
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Global dynamics for a multi-group alcoholism model with public health education and alcoholism age
Shuang-Hong Ma, Hai-Feng Huo
Mathematical Biosciences and Engineering,2019, 16(3): 1683-1708.doi: 10.3934/mbe.2019080
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Zenab Alrikaby, Xia Liu, Tonghua Zhang, Federico Frascoli
Mathematical Biosciences and Engineering,2019, 16(3): 1729-1749.doi: 10.3934/mbe.2019083
Abstract + HTML + PDF(1173 KB)
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Discrete time darwinian dynamics and semelparity versus iteroparity
J. M. Cushing
Mathematical Biosciences and Engineering,2019, 16(3): 1815-1835.doi: 10.3934/mbe.2019088
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A mathematical model of oncolytic virotherapy with time delay
Zizi Wang, Zhiming Guo, Hal Smith
Mathematical Biosciences and Engineering,2019, 16(3): 1836-1860.doi: 10.3934/mbe.2019089
Abstract + HTML + PDF(935 KB)
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The minimal model of Hahn for the Calvin cycle
Hussein Obeid, Alan D. Rendall
Mathematical Biosciences and Engineering,2019, 16(3): 2353-2370.doi: 10.3934/mbe.2019118
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Hopf bifurcation in a CTL-inclusive HIV-1 infection model with two time delays
Juan Wang, Chunyang Qin, Yuming Chen, Xia Wang
Mathematical Biosciences and Engineering,2019, 16(3): 2587-2612.doi: 10.3934/mbe.2019130
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Muntaser Safan
Mathematical Biosciences and Engineering,2019, 16(3): 2613-2649.doi: 10.3934/mbe.2019131
Abstract + HTML + PDF(1525 KB)
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The impacts of dispersal on the competition outcome of multi-patch competition models
Ali Mai, Guowei Sun, LinWang
Mathematical Biosciences and Engineering,2019, 16(3): 2697-2716.doi: 10.3934/mbe.2019134
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Homologous recombination defects and how they affect replication fork maintenance
Mi Young Son, Paul Hasty
AIMS Genetics,2018, 5(3): 192-211.doi: 10.3934/genet.2018.4.192
Abstract + HTML + PDF(491 KB)
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Bifurcation analysis of a pair-wise epidemic model on adaptive networks
Jinna Lu, Xiaoguang Zhang
Mathematical Biosciences and Engineering,2019, 16(3): 2973-2989.doi: 10.3934/mbe.2019147
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A diffusive SIS epidemic model in a heterogeneous and periodically evolvingenvironment
Liqiong Pu, Zhigui Lin
Mathematical Biosciences and Engineering,2019, 16(3): 3094-3110.doi: 10.3934/mbe.2019153
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Global dynamics of a multi-stage brucellosis model with distributed delays and indirect transmission
Qiang Hou, Haiyan Qin
Mathematical Biosciences and Engineering,2019, 16(3): 3111-3129.doi: 10.3934/mbe.2019154
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Effects of limited volatiles release by plants in tritrophic interactions
Bruno Buonomo , Francesco Giannino , Stéphanie Saussure , Ezio Venturino
Mathematical Biosciences and Engineering,2019, 16(3): 3331-3344.doi: 10.3934/mbe.2019166
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The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis
Rong Qiang, Wanbiao Ma , Ke Guo, Hongwu Du
Mathematical Biosciences and Engineering,, (3): 3488-3511.doi: 10.3934/mbe.2019175
Abstract + HTML + PDF(908 KB)
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Modelling and analysis of an alcoholism model with treatment and effect of Twitter
Hai-Feng Huo, Shuang-Lin Jing, Xun-Yang Wang, Hong Xiang
Mathematical Biosciences and Engineering,2019, 16(3): 3561-3622.doi: 10.3934/mbe.2019179
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The stochastic extinction and stability conditions for nonlinear malaria epidemics
Divine Wanduku
Mathematical Biosciences and Engineering,2019, 16(3): 3771-3806.doi: 10.3934/mbe.2019187
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Zhichao Jiang, Xiaohua Bi, Tongqian Zhang, B.G. Sampath Aruna Pradeep
Mathematical Biosciences and Engineering,2019, 16(3): 3807-3829.doi: 10.3934/mbe.2019188
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Salihu Sabiu Musa, Shi Zhao, Hei-Shen Chan, Zhen Jin, Daihai He
Mathematical Biosciences and Engineering,2019, 16(3): 3841-3863.doi: 10.3934/mbe.2019190
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Metastability of solitary waves in diatomic FPUT lattices
Nickolas Giardetti, Amy Shapiro, Stephen Windle, J. Douglas Wright
Mathematics in Engineering,2019, 1(3): 419-433.doi: 10.3934/mine.2019.3.419
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Bifurcation structure of nonconstant positive steady states for a diffusive predator-prey model
Dongfu Tong, Yongli Cai, Bingxian Wang, Weiming Wang
Mathematical Biosciences and Engineering,2019, 16(3): 3988-4006.doi: 10.3934/mbe.2019197
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Discontinuous solutions for the short-pulse master mode-locking equation
Giuseppe Maria Coclite, Lorenzo di Ruvo
AIMS Mathematics,2019, 4(3): 437-462.doi: 10.3934/math.2019.3.437
Abstract + HTML + PDF(365 KB)
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Eduardo González-Olivares, Claudio Arancibia-Ibarra, Alejandro Rojas-Palma, Betsabé González-Yañez
Mathematical Biosciences and Engineering,2019, 16(3): 4274-4298.doi: 10.3934/mbe.2019213
Abstract + HTML + PDF(1433 KB)
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The effect of the needle exchange program on the spread of some sexually transmitted diseases
Eliza Bánhegyi, Attila Dénes, János Karsai, László Székely
Mathematical Biosciences and Engineering,2019, 16(3): 4506-4525.doi: 10.3934/mbe.2019225
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Banking market competition in Europe—financial stability or fragility enhancing?
Kalle Ahi, Laivi Laidroo
Quantitative Finance and Economics,2019, 3(3): 257-285.doi: 10.3934/QFE.2019.2.257
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Dynamics of a malaria infection model with time delay
Qian Ding, Jian Liu, Zhiming Guo
Mathematical Biosciences and Engineering,2019, 16(3): 4885-4907.doi: 10.3934/mbe.2019246
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Yanjie Hong, Wanbiao Ma
Mathematical Biosciences and Engineering,2019, 16(3): 4936-4946.doi: 10.3934/mbe.2019249
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Fear effect in prey and hunting cooperation among predators in a Leslie-Gower model
Saheb Pal, Nikhil Pal, Sudip Samanta, Joydev Chattopadhyay
Mathematical Biosciences and Engineering,2019, 16(3): 5146-5179.doi: 10.3934/mbe.2019258
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A cholera transmission model incorporating the impact of medical resources
Chayu Yang, Jin Wang
Mathematical Biosciences and Engineering,2019, 16(3): 5226-5246.doi: 10.3934/mbe.2019261
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Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions
Pei Yu, Xiangyu Wang
Mathematical Biosciences and Engineering,, (3): 5263-5286.doi: 10.3934/mbe.2019263
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Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions
Pei Yu, Xiangyu Wang
Mathematical Biosciences and Engineering,, (3): 5263-5286.doi: 10.3934/mbe.2019263
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Analysis on recurrence behavior in oscillating networks of biologically relevant organic reactions
Pei Yu, Xiangyu Wang
Mathematical Biosciences and Engineering,2019, 16(3): 5263-5286.doi: 10.3934/mbe.2019263
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The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis
Rong Qiang, Wanbiao Ma, Ke Guo, Hongwu Du
Mathematical Biosciences and Engineering,2019, 16(3): 3488-3511.doi: 10.3934/mbe.2019175
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Dynamics of an SLIR model with nonmonotone incidence rate and stochastic perturbation
Jinhui Zhang, Jingli Ren, Xinan Zhang
Mathematical Biosciences and Engineering,2019, 16(3): 5504-5530.doi: 10.3934/mbe.2019274
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Time-delayed model of autoimmune dynamics
Farzad Fatehi, Yuliya N. Kyrychko, Konstantin B. Blyuss
Mathematical Biosciences and Engineering,2019, 16(3): 5613-5639.doi: 10.3934/mbe.2019279
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Asymptotic analysis of endemic equilibrium to a brucellosis model
Mingtao Li, Xin Pei, Juan Zhang, Li Li
Mathematical Biosciences and Engineering,2019, 16(3): 5836-5850.doi: 10.3934/mbe.2019291
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Xiao Tu, Qinran Zhang, Wei Zhang, Xiufen Zou
Mathematical Biosciences and Engineering,2019, 16(3): 5877-5896.doi: 10.3934/mbe.2019294
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Dynamic analysis of the recurrent epidemic model
Hui Cao, Dongxue Yan, Ao Li
Mathematical Biosciences and Engineering,2019, 16(3): 5972-5990.doi: 10.3934/mbe.2019299
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The impact of media converge on complex networks on disease transmission
Maoxing Liu, Shushu He, Yongzheng Sun
Mathematical Biosciences and Engineering,2019, 16(3): 6335-6349.doi: 10.3934/mbe.2019316
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Zigen Song, Jian Xu, Bin Zhen
Mathematical Biosciences and Engineering,2019, 16(3): 6406-6425.doi: 10.3934/mbe.2019320
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The price adjustment equation with different types of conformable derivatives in market equilibrium
Erdal Bas, Bahar Acay, Ramazan Ozarslan
AIMS Mathematics,2019, 4(3): 805-820.doi: 10.3934/math.2019.3.805
Abstract + HTML + PDF(429 KB)
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Ting Guo, Zhipeng Qiu
Mathematical Biosciences and Engineering,2019, 16(3): 6822-6841.doi: 10.3934/mbe.2019341
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Shunyi Li
Mathematical Biosciences and Engineering,2019, 16(3): 6934-6961.doi: 10.3934/mbe.2019348
Abstract + HTML + PDF(4811 KB)
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A thorough look at the (in)stability of piston-theoretic beams
Jason Howell, Katelynn Huneycutt, Justin T. Webster, Spencer Wilder
Mathematics in Engineering,2019, 1(3): 614-647.doi: 10.3934/mine.2019.3.614
Abstract + HTML + PDF(3399 KB)
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On the mechanism of antibiotic resistance and fecal microbiota transplantation
Xiaxia Kang, Jie Yan, Fan Huang, Ling Yang
Mathematical Biosciences and Engineering,2019, 16(3): 7057-7084.doi: 10.3934/mbe.2019354
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Modeling epidemic in metapopulation networks with heterogeneous diffusion rates
Maoxing Liu, Jie Zhang, Zhengguang Li, Yongzheng Sun
Mathematical Biosciences and Engineering,2019, 16(3): 7085-7097.doi: 10.3934/mbe.2019355
Abstract + HTML + PDF(5161 KB)
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Davide De Gaetano
Mathematical Biosciences and Engineering,2019, 16(3): 7195-7216.doi: 10.3934/mbe.2019361
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Oscillation threshold for a mosquito population suppression model with time delay
Yuanxian Hui, Genghong Lin, Qiwen Sun
Mathematical Biosciences and Engineering,2019, 16(3): 7362-7374.doi: 10.3934/mbe.2019367
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Shihe Xu, Junde Wu
Mathematical Biosciences and Engineering,2019, 16(3): 7433-7446.doi: 10.3934/mbe.2019372
Abstract + HTML + PDF(654 KB)
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Constructing a stable complex index of a system’s quality for a series of observations
Tatyana V. Zhgun
National Accounting Review,2019, 1(3): 42-61.doi: 10.3934/NAR.2019.1.42
Abstract + HTML + PDF(1512 KB)
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Mathematical analysis of an age-structured HIV-1 infection model with CTL immune response
Xiaohong Tian, Rui Xu, Jiazhe Lin
Mathematical Biosciences and Engineering,2019, 16(3): 7850-7882.doi: 10.3934/mbe.2019395
Abstract + HTML + PDF(1977 KB)
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Eduardo González-Olivares, Claudio Arancibia-Ibarra, Alejandro Rojas-Palma, Betsabé González-Yañez
Mathematical Biosciences and Engineering,2019, 16(3): 7995-8024.doi: 10.3934/mbe.2019403
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Mathematical analysis of the Cancitis model and the role of inflammation in blood cancer progression
Zamra Sajid, Morten Andersen, Johnny T. Ottesen
Mathematical Biosciences and Engineering,2019, 16(3): 8268-8289.doi: 10.3934/mbe.2019418
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Conditionally stable unique continuation and applications to thermoacoustic tomography
Plamen Stefanov
Mathematics in Engineering,2019, 1(3): 789-799.doi: 10.3934/mine.2019.4.789
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Behzad Ghanbari, Mustafa Inc, Abdullahi Yusuf, Dumitru Baleanu
AIMS Mathematics,2019, 4(3): 1523-1539.doi: 10.3934/math.2019.6.1523
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Tongqian Zhang, Ning Gao, Tengfei Wang, Hongxia Liu, Zhichao Jiang
Mathematical Biosciences and Engineering,2020, 17(3): 179-201.doi: 10.3934/mbe.2020010
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Balázs Boros, Stefan Müller, Georg Regensburger
Mathematical Biosciences and Engineering,2020, 17(3): 442-459.doi: 10.3934/mbe.2020024
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Orbital stability of periodic solutions of an impulsive system with a linear continuous-time part
Alexander N. Churilov
AIMS Mathematics,2020, 5(3): 96-110.doi: 10.3934/math.2020007
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N. H. AlShamrani, A. M. Elaiw
Mathematical Biosciences and Engineering,2020, 17(3): 575-605.doi: 10.3934/mbe.2020030
Abstract + HTML + PDF(2721 KB)
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Yu Chen, Jin Cheng, Giuseppe Floridia, Youichiro Wada, Masahiro Yamamoto
Mathematics in Engineering,2020, 2(3): 26-33.doi: 10.3934/mine.2020002
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A black swan and canard cascades in an SIR infectious disease model
Andrei Korobeinikov, Elena Shchepakina, Vladimir Sobolev
Mathematical Biosciences and Engineering,2020, 17(3): 725-736.doi: 10.3934/mbe.2020037
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Shadrack Mubanga Chisenga, Tilahun Seyoum Workneh, Geremew Bultosa, Mark Laing
AIMS Agriculture and Food,2019, 4(3): 939-966.doi: 10.3934/agrfood.2019.4.939
Abstract + HTML + PDF(787 KB)
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Mostafa Adimy, Abdennasser Chekroun, Claudia Pio Ferreira
Mathematical Biosciences and Engineering,2020, 17(3): 1329-1354.doi: 10.3934/mbe.2020067
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Nayyar Mehmood, Niaz Ahmad
AIMS Mathematics,2020, 5(3): 385-398.doi: 10.3934/math.2020026
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Global stability analysis of a viral infection model in a critical case
Wei Wang, Xiulan Lai
Mathematical Biosciences and Engineering,2020, 17(3): 1442-1449.doi: 10.3934/mbe.2020074
Abstract + HTML + PDF(595 KB)
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Ran Zhang, Shengqiang Liu
Mathematical Biosciences and Engineering,2020, 17(3): 1450-1478.doi: 10.3934/mbe.2020075
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Mechanical properties of hot-mix asphalt using waste crumber rubber and phenol formaldehyde polymer
Mushtaq Ahmad, Salmia Beddu, Shah Hussain, Aneel Manan, Zarina binti Itam
AIMS Materials Science,2019, 6(3): 1164-1175.doi: 10.3934/matersci.2019.6.1164
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Albert Henry Ntarmah, Yusheng Kong, Michael Kobina Gyan
Quantitative Finance and Economics,2019, 3(3): 709-738.doi: 10.3934/QFE.2019.4.709
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Periodic mild solutions of impulsive fractional evolution equations
Lulu Ren, JinRong Wang, Michal Fečkan
AIMS Mathematics,2020, 5(3): 497-506.doi: 10.3934/math.2020033
Abstract + HTML + PDF(228 KB)