
-
Previous Article
Optimal vaccination strategies for an SEIR model of infectious diseases with logistic growth
- MBE Home
- This Issue
-
Next Article
A network model for control of dengue epidemic using sterile insect technique
Spatially-implicit modelling of disease-behaviour interactions in the context of non-pharmaceutical interventions
1. | Botswana International University of Science and Technology, Department of Mathematics and Statistical Sciences, Private Bag 16, Palapye, Botswana |
2. | University of Waterloo, Department of Applied Mathematics, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada |
Pair approximation models have been used to study the spread of infectious diseases in spatially distributed host populations, and to explore disease control strategies such as vaccination and case isolation. Here we introduce a pair approximation model of individual uptake of non-pharmaceutical interventions (NPIs) for an acute self-limiting infection, where susceptible individuals can learn the NPIs either from other susceptible individuals who are already practicing NPIs ("social learning"), or their uptake of NPIs can be stimulated by being neighbours of an infectious person ("exposure learning"). NPIs include individual measures such as hand-washing and respiratory etiquette. Individuals can also drop the habit of using NPIs at a certain rate. We derive a spatially defined expression of the basic reproduction number $R_0$ and we also numerically simulate the model equations. We find that exposure learning is generally more efficient than social learning, since exposure learning generates NPI uptake in the individuals at immediate risk of infection. However, if social learning is pre-emptive, beginning a sufficient amount of time before the epidemic, then it can be more effective than exposure learning. Interestingly, varying the initial number of individuals practicing NPIs does not significantly impact the epidemic final size. Also, if initial source infections are surrounded by protective individuals, there are parameter regimes where increasing the initial number of source infections actually decreases the infection peak (instead of increasing it) and makes it occur sooner. The peak prevalence increases with the rate at which individuals drop the habit of using NPIs, but the response of peak prevalence to changes in the forgetting rate are qualitatively different for the two forms of learning. The pair approximation methodology developed here illustrates how analytical approaches for studying interactions between social processes and disease dynamics in a spatially structured population should be further pursued.
References:
[1] |
K. A. Alexander and J. W. McNutt, Human behavior influences infectious disease emergence at the human-animal interface, Frontiers in Ecology and the Environment, 8 (2010), 522-526. Google Scholar |
[2] |
M. C. Auld, Estimating behavioral response to the AIDS epidemic, Contributions to Economic Analysis and Policy 5 (2006), Art. 12. Google Scholar |
[3] |
N. Bacaer,
Approximation of the basic reproduction number for vector-borne disease with periodic vector population, Bulleting of Mathematical Biology, 69 (2007), 1067-1091.
doi: 10.1007/s11538-006-9166-9. |
[4] |
C. T. Bauch,
A versatile ODE approximation to a network model for the spread of sexually transmitted diseases, Journal of Mathematical Biology, 45 (2002), 375-395.
doi: 10.1007/s002850200153. |
[5] |
C. T. Bauch,
The spread of infectious diseases in spatially structured populations: An invasory pair approximation, Mathematical Biosciences, 198 (2005), 217-237.
doi: 10.1016/j.mbs.2005.06.005. |
[6] |
C. T. Bauch, A. d'Onofrio and P. Manfredi,
Behavioral epidemiology of infectious diseases: An overview, Modeling the interplay between human behavior and the spread of infectious diseases, Springer-Verlag, (2013), 1-19.
doi: 10.1007/978-1-4614-5474-8_1. |
[7] |
C. T. Bauch and A. P. Galvani,
Using network models to approximate spatial point-process models, Mathematical Biosciences, 184 (2003), 101-114.
doi: 10.1016/S0025-5564(03)00042-7. |
[8] |
C. T. Bauch and D. A. Rand,
A moment closure model for sexually transmitted disease transmission through a concurrent partnership network, The Royal Society, 267 (2000), 2019-2027.
doi: 10.1098/rspb.2000.1244. |
[9] |
J. Benoit, A. Nunes and M. Telo da Gama,
Pair approximation models for disease spread, The European Physical Journal B, 50 (2006), 177-181.
doi: 10.1140/epjb/e2006-00096-x. |
[10] |
K. Dietz,
The estimation of the basic reproduction number for infectious diseases, Statistical Methods in Medical Research, 2 (1993), 23-41.
doi: 10.1177/096228029300200103. |
[11] |
S. P. Ellner,
Pair approximation for lattice models with multiple interaction scales, Journal of Theoretical Biology, 210 (2001), 435-447.
doi: 10.1006/jtbi.2001.2322. |
[12] |
E. P. Fenichel, C. Castillo-Chavez, M. G. Geddia, G. Chowell, P. A. Gonzalez Parra, G. J. Hickling, G. Holloway, R. Horan, B. Morin, C. Perrings, M. Springborn, L. Velazquez and C. Villalobos,
Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences, 108 (2011), 6306-6311.
doi: 10.1073/pnas.1011250108. |
[13] |
N. M. Ferguson, C. A. Donnelly and R. M. Anderson,
The foot and mouth epidemic in Great Britain: pattern of spread and impact of interventions, Science, 292 (2001), 1155-1160.
doi: 10.1126/science.1061020. |
[14] |
M. J. Ferrari, S. Bansal, L. A. Meyers and O. N. Bjϕrnstad, Network frailty and the geometry of head immunity, Proceedings of the Royal Society B, 273 (2006), 2743-2748. Google Scholar |
[15] |
S. Funk, E. Gilad, C. Watkins and V. A. A. Jansen,
The spread of awareness and its impact on epidemic outbreaks, Proceedings of the National Academy of Sciences, 106 (2009), 6872-6877.
doi: 10.1073/pnas.0810762106. |
[16] |
R. J. Glass, L. M. Glass, W. E. Beyeler and H. J. Min, Targeted social distancing designs for pandemic influenza, Emerging Infectious Diseases, 12 (2016), 1671-1681. Google Scholar |
[17] |
D. Hiebeler,
Moment equations and dynamics of a household SIS epidemiological model, Bulletin of Mathematical Biology, 68 (2006), 1315-1333.
doi: 10.1007/s11538-006-9080-1. |
[18] |
M. J. Keeling,
The effects of local spatial structure on epidemiological invasions, Proceedings of The Royal Society of London B, 266 (1999), 859-867.
doi: 10.1098/rspb.1999.0716. |
[19] |
M.J. Keeling, D. A. Rand and A. J. Morris,
Correlation models for childhood epidemics, Proceedings of The Royal Society of London B, 264 (1997), 1149-1156.
doi: 10.1098/rspb.1997.0159. |
[20] |
J. Li, D. Blakeley and R. J. Smith,
The failure of $\mathbb{R}_0$, Computational and Mathematical Methods in Medicine, 12 (2011), 1-17.
|
[21] |
C. N. L. Macpherson, Human behavior and the epidemiology of parasitic zoonoses, International Journal for Parasitology, 35 (2005), 1319-1331. Google Scholar |
[22] |
S. Maharaj and A. Kleczkowski,
Controlling epidemic spread by social distancing: Do it well or not at all, BMC Public Health, 12 (2012), p679.
doi: 10.1186/1471-2458-12-679. |
[23] |
L. Mao and Y. Yang,
Coupling infectious diseases, human preventive behavior, and networks--a conceptual framework for epidemic modeling, Social Science Medicine, 74 (2012), 167-175.
doi: 10.1016/j.socscimed.2011.10.012. |
[24] |
J. P. McGowan, S. S. Shah, C. E. Ganea, S. Blum, J. A. Ernst, K. L. Irwin, N. Olivo and P. J. Weidle,
Risk behavior for transmission of Human Immunodeficiency Virus (HIV) among HIV-seropositive individuals in an urban setting, Clinical Infectious Diseases, 38 (2004), 122-127.
doi: 10.1086/380128. |
[25] |
T. Modie-Moroka,
Intimate partner violence and sexually risky behavior in Botswana: Implications for HIV prevention, Health Care for Women International, 30 (2009), 230-231.
doi: 10.1080/07399330802662036. |
[26] |
S. S. Morse,
Factors in the emergence of infectious diseases, Factors in the Emergence of Infectious Diseases, (2001), 8-26.
doi: 10.1057/9780230524248_2. |
[27] |
S. Mushayabasa, C. P. Bhunu and M. Dhlamini, Impact of vaccination and culling on controlling foot and mouth disease: A mathematical modeling approach, World of Journal Vaccines, 1 (2011), 156-161. Google Scholar |
[28] |
S. O. Oyeyemi, E. Gabarron and R. Wynn,
Ebola, Twitter, and misinformation: A dangerous combination?, British Medical Journal, 349 (2014), g6178.
doi: 10.1136/bmj.g6178. |
[29] |
P. E. Parham and N. M. Ferguson,
Space and contact networks: Capturing of the locality of disease transmission, Journal of Royal Society, 3 (2005), 483-493.
doi: 10.1098/rsif.2005.0105. |
[30] |
P. E. Parham, B. K. Singh and N. M. Ferguson, Analytical approximation of spatial epidemic models of foot and mouth disease, Theoretical Population Biology, 72 (2008), 349-368. Google Scholar |
[31] |
F. M. Pillemer, R. J. Blendon, A. M. Zaslavsky and B. Y. Lee, Predicting support for non-pharmaceutical interventions during infectious outbreaks: A four region analysis, Disasters, 39 (2014), 125-145. Google Scholar |
[32] |
D. A. Rand, Correlation equations and pair approximations for spatial ecologies, CWI Quarterly, 12 (1999), 329-368. Google Scholar |
[33] |
C. T. Reluga, Game theory of social distancing in response to an epidemic Plos Computational Biology 6 (2010), e1000793, 9pp.
doi: 10.1371/journal.pcbi.1000793. |
[34] |
N. Ringa and C. T. Bauch,
Dynamics and control of foot and mouth disease in endemic countries: A pair approximation model, Journal of Theoretical Biology, 357 (2014), 150-159.
doi: 10.1016/j.jtbi.2014.05.010. |
[35] |
A. Rizzo, M. Frasca and M. Porfiri,
Effect of individual behavior on epidemic spreading in activity-driven networks, Physical Review E, 90 (2014), 042801.
doi: 10.1103/PhysRevE.90.042801. |
[36] |
M. Salathe and S. Bonhoeffer,
The effect of opinion clustering on disease outbreaks, Journal of The Royal Society Interface, 5 (2008), 1505-1508.
doi: 10.1098/rsif.2008.0271. |
[37] |
L. B. Shaw and I. B. Schwartz,
Fluctuating epidemics on adaptive networks, Physical Review E, 77 (2008), 066101, 10pp.
doi: 10.1103/PhysRevE.77.066101. |
[38] |
R. L. Stoneburner and D. Low-Beer,
Population-level HIV decline and behavioral risk avoidance in Uganda, Science, 304 (2004), 714-718.
doi: 10.1126/science.1093166. |
[39] |
R. R. Swenson, W. S. Hadley, C. D. Houck, S. K. Dance and L. K. Brown,
Who accepts a rapid HIV antibody test? The role of race/ethnicity and HIV risk behavior among community adolescents, Journal of Adolescent Health, 48 (2011), 527-529.
doi: 10.1016/j.jadohealth.2010.08.013. |
[40] |
J. M. Tchuenche and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission ISRN Biomathematics2012 (2012), Article ID 581274, 10pp.
doi: 10.5402/2012/581274. |
show all references
References:
[1] |
K. A. Alexander and J. W. McNutt, Human behavior influences infectious disease emergence at the human-animal interface, Frontiers in Ecology and the Environment, 8 (2010), 522-526. Google Scholar |
[2] |
M. C. Auld, Estimating behavioral response to the AIDS epidemic, Contributions to Economic Analysis and Policy 5 (2006), Art. 12. Google Scholar |
[3] |
N. Bacaer,
Approximation of the basic reproduction number for vector-borne disease with periodic vector population, Bulleting of Mathematical Biology, 69 (2007), 1067-1091.
doi: 10.1007/s11538-006-9166-9. |
[4] |
C. T. Bauch,
A versatile ODE approximation to a network model for the spread of sexually transmitted diseases, Journal of Mathematical Biology, 45 (2002), 375-395.
doi: 10.1007/s002850200153. |
[5] |
C. T. Bauch,
The spread of infectious diseases in spatially structured populations: An invasory pair approximation, Mathematical Biosciences, 198 (2005), 217-237.
doi: 10.1016/j.mbs.2005.06.005. |
[6] |
C. T. Bauch, A. d'Onofrio and P. Manfredi,
Behavioral epidemiology of infectious diseases: An overview, Modeling the interplay between human behavior and the spread of infectious diseases, Springer-Verlag, (2013), 1-19.
doi: 10.1007/978-1-4614-5474-8_1. |
[7] |
C. T. Bauch and A. P. Galvani,
Using network models to approximate spatial point-process models, Mathematical Biosciences, 184 (2003), 101-114.
doi: 10.1016/S0025-5564(03)00042-7. |
[8] |
C. T. Bauch and D. A. Rand,
A moment closure model for sexually transmitted disease transmission through a concurrent partnership network, The Royal Society, 267 (2000), 2019-2027.
doi: 10.1098/rspb.2000.1244. |
[9] |
J. Benoit, A. Nunes and M. Telo da Gama,
Pair approximation models for disease spread, The European Physical Journal B, 50 (2006), 177-181.
doi: 10.1140/epjb/e2006-00096-x. |
[10] |
K. Dietz,
The estimation of the basic reproduction number for infectious diseases, Statistical Methods in Medical Research, 2 (1993), 23-41.
doi: 10.1177/096228029300200103. |
[11] |
S. P. Ellner,
Pair approximation for lattice models with multiple interaction scales, Journal of Theoretical Biology, 210 (2001), 435-447.
doi: 10.1006/jtbi.2001.2322. |
[12] |
E. P. Fenichel, C. Castillo-Chavez, M. G. Geddia, G. Chowell, P. A. Gonzalez Parra, G. J. Hickling, G. Holloway, R. Horan, B. Morin, C. Perrings, M. Springborn, L. Velazquez and C. Villalobos,
Adaptive human behavior in epidemiological models, Proceedings of the National Academy of Sciences, 108 (2011), 6306-6311.
doi: 10.1073/pnas.1011250108. |
[13] |
N. M. Ferguson, C. A. Donnelly and R. M. Anderson,
The foot and mouth epidemic in Great Britain: pattern of spread and impact of interventions, Science, 292 (2001), 1155-1160.
doi: 10.1126/science.1061020. |
[14] |
M. J. Ferrari, S. Bansal, L. A. Meyers and O. N. Bjϕrnstad, Network frailty and the geometry of head immunity, Proceedings of the Royal Society B, 273 (2006), 2743-2748. Google Scholar |
[15] |
S. Funk, E. Gilad, C. Watkins and V. A. A. Jansen,
The spread of awareness and its impact on epidemic outbreaks, Proceedings of the National Academy of Sciences, 106 (2009), 6872-6877.
doi: 10.1073/pnas.0810762106. |
[16] |
R. J. Glass, L. M. Glass, W. E. Beyeler and H. J. Min, Targeted social distancing designs for pandemic influenza, Emerging Infectious Diseases, 12 (2016), 1671-1681. Google Scholar |
[17] |
D. Hiebeler,
Moment equations and dynamics of a household SIS epidemiological model, Bulletin of Mathematical Biology, 68 (2006), 1315-1333.
doi: 10.1007/s11538-006-9080-1. |
[18] |
M. J. Keeling,
The effects of local spatial structure on epidemiological invasions, Proceedings of The Royal Society of London B, 266 (1999), 859-867.
doi: 10.1098/rspb.1999.0716. |
[19] |
M.J. Keeling, D. A. Rand and A. J. Morris,
Correlation models for childhood epidemics, Proceedings of The Royal Society of London B, 264 (1997), 1149-1156.
doi: 10.1098/rspb.1997.0159. |
[20] |
J. Li, D. Blakeley and R. J. Smith,
The failure of $\mathbb{R}_0$, Computational and Mathematical Methods in Medicine, 12 (2011), 1-17.
|
[21] |
C. N. L. Macpherson, Human behavior and the epidemiology of parasitic zoonoses, International Journal for Parasitology, 35 (2005), 1319-1331. Google Scholar |
[22] |
S. Maharaj and A. Kleczkowski,
Controlling epidemic spread by social distancing: Do it well or not at all, BMC Public Health, 12 (2012), p679.
doi: 10.1186/1471-2458-12-679. |
[23] |
L. Mao and Y. Yang,
Coupling infectious diseases, human preventive behavior, and networks--a conceptual framework for epidemic modeling, Social Science Medicine, 74 (2012), 167-175.
doi: 10.1016/j.socscimed.2011.10.012. |
[24] |
J. P. McGowan, S. S. Shah, C. E. Ganea, S. Blum, J. A. Ernst, K. L. Irwin, N. Olivo and P. J. Weidle,
Risk behavior for transmission of Human Immunodeficiency Virus (HIV) among HIV-seropositive individuals in an urban setting, Clinical Infectious Diseases, 38 (2004), 122-127.
doi: 10.1086/380128. |
[25] |
T. Modie-Moroka,
Intimate partner violence and sexually risky behavior in Botswana: Implications for HIV prevention, Health Care for Women International, 30 (2009), 230-231.
doi: 10.1080/07399330802662036. |
[26] |
S. S. Morse,
Factors in the emergence of infectious diseases, Factors in the Emergence of Infectious Diseases, (2001), 8-26.
doi: 10.1057/9780230524248_2. |
[27] |
S. Mushayabasa, C. P. Bhunu and M. Dhlamini, Impact of vaccination and culling on controlling foot and mouth disease: A mathematical modeling approach, World of Journal Vaccines, 1 (2011), 156-161. Google Scholar |
[28] |
S. O. Oyeyemi, E. Gabarron and R. Wynn,
Ebola, Twitter, and misinformation: A dangerous combination?, British Medical Journal, 349 (2014), g6178.
doi: 10.1136/bmj.g6178. |
[29] |
P. E. Parham and N. M. Ferguson,
Space and contact networks: Capturing of the locality of disease transmission, Journal of Royal Society, 3 (2005), 483-493.
doi: 10.1098/rsif.2005.0105. |
[30] |
P. E. Parham, B. K. Singh and N. M. Ferguson, Analytical approximation of spatial epidemic models of foot and mouth disease, Theoretical Population Biology, 72 (2008), 349-368. Google Scholar |
[31] |
F. M. Pillemer, R. J. Blendon, A. M. Zaslavsky and B. Y. Lee, Predicting support for non-pharmaceutical interventions during infectious outbreaks: A four region analysis, Disasters, 39 (2014), 125-145. Google Scholar |
[32] |
D. A. Rand, Correlation equations and pair approximations for spatial ecologies, CWI Quarterly, 12 (1999), 329-368. Google Scholar |
[33] |
C. T. Reluga, Game theory of social distancing in response to an epidemic Plos Computational Biology 6 (2010), e1000793, 9pp.
doi: 10.1371/journal.pcbi.1000793. |
[34] |
N. Ringa and C. T. Bauch,
Dynamics and control of foot and mouth disease in endemic countries: A pair approximation model, Journal of Theoretical Biology, 357 (2014), 150-159.
doi: 10.1016/j.jtbi.2014.05.010. |
[35] |
A. Rizzo, M. Frasca and M. Porfiri,
Effect of individual behavior on epidemic spreading in activity-driven networks, Physical Review E, 90 (2014), 042801.
doi: 10.1103/PhysRevE.90.042801. |
[36] |
M. Salathe and S. Bonhoeffer,
The effect of opinion clustering on disease outbreaks, Journal of The Royal Society Interface, 5 (2008), 1505-1508.
doi: 10.1098/rsif.2008.0271. |
[37] |
L. B. Shaw and I. B. Schwartz,
Fluctuating epidemics on adaptive networks, Physical Review E, 77 (2008), 066101, 10pp.
doi: 10.1103/PhysRevE.77.066101. |
[38] |
R. L. Stoneburner and D. Low-Beer,
Population-level HIV decline and behavioral risk avoidance in Uganda, Science, 304 (2004), 714-718.
doi: 10.1126/science.1093166. |
[39] |
R. R. Swenson, W. S. Hadley, C. D. Houck, S. K. Dance and L. K. Brown,
Who accepts a rapid HIV antibody test? The role of race/ethnicity and HIV risk behavior among community adolescents, Journal of Adolescent Health, 48 (2011), 527-529.
doi: 10.1016/j.jadohealth.2010.08.013. |
[40] |
J. M. Tchuenche and C. T. Bauch, Dynamics of an infectious disease where media coverage influences transmission ISRN Biomathematics2012 (2012), Article ID 581274, 10pp.
doi: 10.5402/2012/581274. |








(a) General expression of |
Equation (10) |
(b) Expression of |
Equation (17) |
(c) Simplification of |
Equation (18) |
(d) Simplification of |
Equation(19) |
(e) Simplification of |
Equation (20) |
(f) Simplification of |
Equation(21) |
(g) Simplification of |
Equation (22) |
(h) Simplification of |
Equation (23) |
(a) General expression of |
Equation (10) |
(b) Expression of |
Equation (17) |
(c) Simplification of |
Equation (18) |
(d) Simplification of |
Equation(19) |
(e) Simplification of |
Equation (20) |
(f) Simplification of |
Equation(21) |
(g) Simplification of |
Equation (22) |
(h) Simplification of |
Equation (23) |
[1] |
Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020339 |
[2] |
Bernard Bonnard, Jérémy Rouot. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model. Journal of Geometric Mechanics, 2020 doi: 10.3934/jgm.2020032 |
[3] |
Imam Wijaya, Hirofumi Notsu. Stability estimates and a Lagrange-Galerkin scheme for a Navier-Stokes type model of flow in non-homogeneous porous media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1197-1212. doi: 10.3934/dcdss.2020234 |
[4] |
Yu-Jhe Huang, Zhong-Fu Huang, Jonq Juang, Yu-Hao Liang. Flocking of non-identical Cucker-Smale models on general coupling network. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1111-1127. doi: 10.3934/dcdsb.2020155 |
[5] |
Ziang Long, Penghang Yin, Jack Xin. Global convergence and geometric characterization of slow to fast weight evolution in neural network training for classifying linearly non-separable data. Inverse Problems & Imaging, 2021, 15 (1) : 41-62. doi: 10.3934/ipi.2020077 |
[6] |
Simone Göttlich, Elisa Iacomini, Thomas Jung. Properties of the LWR model with time delay. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2020032 |
[7] |
Ténan Yeo. Stochastic and deterministic SIS patch model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021012 |
[8] |
M. Dambrine, B. Puig, G. Vallet. A mathematical model for marine dinoflagellates blooms. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 615-633. doi: 10.3934/dcdss.2020424 |
[9] |
Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020457 |
[10] |
Laurent Di Menza, Virginie Joanne-Fabre. An age group model for the study of a population of trees. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020464 |
[11] |
Eduard Feireisl, Elisabetta Rocca, Giulio Schimperna, Arghir Zarnescu. Weak sequential stability for a nonlinear model of nematic electrolytes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 219-241. doi: 10.3934/dcdss.2020366 |
[12] |
Yu Jin, Xiang-Qiang Zhao. The spatial dynamics of a Zebra mussel model in river environments. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020362 |
[13] |
Yunfeng Geng, Xiaoying Wang, Frithjof Lutscher. Coexistence of competing consumers on a single resource in a hybrid model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 269-297. doi: 10.3934/dcdsb.2020140 |
[14] |
Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond. A new model for the emergence of blood capillary networks. Networks & Heterogeneous Media, 2020 doi: 10.3934/nhm.2021001 |
[15] |
Mingchao Zhao, You-Wei Wen, Michael Ng, Hongwei Li. A nonlocal low rank model for poisson noise removal. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021003 |
[16] |
Mohamed Dellal, Bachir Bar. Global analysis of a model of competition in the chemostat with internal inhibitor. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1129-1148. doi: 10.3934/dcdsb.2020156 |
[17] |
Jakub Kantner, Michal Beneš. Mathematical model of signal propagation in excitable media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 935-951. doi: 10.3934/dcdss.2020382 |
[18] |
Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020316 |
[19] |
Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020317 |
[20] |
Yining Cao, Chuck Jia, Roger Temam, Joseph Tribbia. Mathematical analysis of a cloud resolving model including the ice microphysics. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 131-167. doi: 10.3934/dcds.2020219 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]