• Previous Article
    Mathematical models of contact patterns between age groups for predicting the spread of infectious diseases
  • MBE Home
  • This Issue
  • Next Article
    The role of multiple modeling perspectives in students' learning of exponential growth
2013, 10(5&6): 1455-1474. doi: 10.3934/mbe.2013.10.1455

The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile

1. 

Mathematical, Computational & Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287

2. 

Department of Epidemiology, Ministerio de Salud, Santiago, Chile

3. 

Universidad del Desarrollo, Santiago, Chile, Chile

4. 

School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287, United States

5. 

Tulane University, New Orleans, LA, 70118, United States

Received  September 2012 Revised  February 2013 Published  August 2013

We use a stochastic simulation model to explore the effect of reactive intervention strategies during the 2002 dengue outbreak in the small population of Easter Island, Chile. We quantified the effect of interventions on the transmission dynamics and epidemic size as a function of the simulated control intensity levels and the timing of initiation of control interventions. Because no dengue outbreaks had been reported prior to 2002 in Easter Island, the 2002 epidemic provided a unique opportunity to estimate the basic reproduction number $R_0$ during the initial epidemic phase, prior to the start of control interventions. We estimated $R_0$ at $27.2$ ($95 \%$CI: $14.8$, $49.3$). We found that the final epidemic size is highly sensitive to the timing of start of interventions. However, even when the control interventions start several weeks after the epidemic onset, reactive intervention efforts can have a significant impact on the final epidemic size. Our results indicate that the rapid implementation of control interventions can have a significant effect in reducing the epidemic size of dengue epidemics.
Citation: Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455
References:
[1]

X. Aguilera, A. Olea, J. Mora, K. Abarca and J. Segovia, Brote de dengue en Isla de Pascua,, El Vigia (Boletín de Vigilancia en Salud Püblica), 16 (2002), 37.   Google Scholar

[2]

R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", Oxford University Press, (1991).  doi: 10.1016/0046-8177(90)90224-S.  Google Scholar

[3]

F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer-Verlag, (2000).  doi: 10.1007/978-1-4614-1686-9.  Google Scholar

[4]

G. Chowell, B. Cazelles, H. Broutin and C. V. Munayco, The influence of climatic and geographic factors on the timing of dengue epidemics in Peru, 1994-2008,, BMC Infectious Diseases, 11 (2011).  doi: 10.1186/1471-2334-11-164.  Google Scholar

[5]

G. Chowell, P. Diaz-Duenas, J. C. Miller, P. W. Fenimore, J. M. Hyman and C. Castillo-Chavez, Estimation of the reproduction number of dengue fever from spatial epidemic data,, Mathematical Biosciences, 208 (2007), 571.  doi: 10.1016/j.mbs.2006.11.011.  Google Scholar

[6]

G. Chowell, C. A. Torre, C. Munyaco-Escate, L. Suarez -Ognio, R. Lopez-Cruz, J. M. Hyman and C. Castillo-Chavez, Spatial and temporal dynamics of dengue fever in Peru: 1994-2006,, Epidemiology and Infection, 8 (2008), 1.  doi: 10.1017/S0950268808000290.  Google Scholar

[7]

G. Chowell and F. Sanchez, Climate-based descriptive models of dengue fever: The 2002 epidemic in Colima, Mexico,, Journal of Environmental Health, 68 (2006), 40.   Google Scholar

[8]

O. Diekmann and J. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation,", Wiley Series in Mathematical and Computational Biology, (2000).   Google Scholar

[9]

, Dirección Meteorológica de Chile., Available from: , ().   Google Scholar

[10]

C. Favier, N. Degallier, M. G. Rosa-Freitas, J. P. Boulanger, J. R. Costa Lima, J. F. Luitgards-Moura, C. E. Menkes, B. Mondet, C. Oliveira, E. T. Weimann and P. Tsouris, Early determination of the reproduction number for vector-borne diseases: The case of dengue in Brazil,, Tropical Medicine and International Health, 11 (2006), 332.  doi: 10.1111/j.1365-3156.2006.01560.x.  Google Scholar

[11]

N. M. Ferguson, C. A. Donnelly and R. M. Anderson, Transmission dynamics and epidemiology of dengue: Insights from age-stratified sero-prevalence surveys,, Phil. Trans. Roy. Soc. Lond. B, 354 (1999), 757.  doi: 10.1098/rstb.1999.0428.  Google Scholar

[12]

D. A. Focks, E. Daniels, D. G. Haile and J. E. Keesling, A simulation model of the epidemiology of urban dengue fever: Literature analysis, model development, preliminary validation, and samples of simulation results,, American Journal of Tropical Medicine and Hygiene, 53 (1995), 489.   Google Scholar

[13]

D. J. Gubler, Dengue and dengue hemorrhagic fever,, Clinical Microbiology Reviews, 11 (1998), 480.   Google Scholar

[14]

L. Gustafsson and M. Sternad, Bringing consistency to simulation of population models-Poisson simulation as a bridge between micro and macro simulation,, Mathematical Biosciences, 209 (2007), 361.  doi: 10.1016/j.mbs.2007.02.004.  Google Scholar

[15]

S. B. Halstead, Dengue virus-mosquito interactions,, Annu Rev Entomol., 53 (2007), 273.  doi: 10.1146/annurev.ento.53.103106.093326.  Google Scholar

[16]

Y. H. Hsieh and C. W. Chen, Turning points, reproduction number, and impact of climatological events for multi-wave dengue outbreaks,, Trop. Med. Int. Health., 14 (2009), 628.  doi: 10.1111/j.1365-3156.2009.02277.x.  Google Scholar

[17]

Y. H. Hsieh and S. Ma, Intervention measures, turning point, and reproduction number for dengue, Singapore, 2005,, American Journal of Tropical Medicine and Hygiene, 80 (2009), 66.   Google Scholar

[18]

J. M. Hyman, J. Li and E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV,, Mathematical Biosciences, 155 (1999), 77.  doi: 10.1016/S0025-5564(98)10057-3.  Google Scholar

[19]

Instituto Nacional de Estadísticas (INE), Estadísticas Demográficas y Vitales, 2009., Available from: , ().   Google Scholar

[20]

J. A. Jacquez, "Compartmental Analysis in Biology and Medicine,", Michigan Thompson-Shore, (1996).   Google Scholar

[21]

T. H. Jetten and D. A. Focks, Potential changes in the distribution of dengue transmission under climate warming,, American Journal Tropical Medicine and Hygiene, 57 (1997), 285.   Google Scholar

[22]

J. S. Koopman, D. R. Prevots, M. A. Vaca Marin, H. Gomez Dantes, M. L. Zarate Aquino, I. M. Longini, Jr and J. Sepulveda Amor, Determinants and predictors of dengue infection in Mexico., American Journal of Epidemiology, 133 (1991), 1168.   Google Scholar

[23]

C. F. Li, T. W. Lim, L. L. Han and R. Fang, Rainfall, abundance of Aedes aegypti and dengue infection in Selangor, Malaysia,, Southeast Asian Journal of Tropical Medicine and Public Health, 16 (1985), 560.   Google Scholar

[24]

P. M. Luz, C. T. Codeco, E. Massad and C. J. Struchiner, Uncertainties regarding dengue modeling in Río de Janeiro, Brazil,, Memórias do Instituto Oswaldo Cruz, 98 (2003), 871.  doi: 10.1590/S0074-02762003000700002.  Google Scholar

[25]

G. MacDonald, "The Epidemiology and Control of Malaria,", Chapter Epidemics, (1957), 45.   Google Scholar

[26]

C. A. Marques, O. P. Forattini and E. Massad, The basic reproduction number for dengue fever in São Paulo state, Brazil: 1990-1991 epidemic,, Transactions of the Royal Society of Tropical Medicine and Hygiene, 88 (1994), 58.   Google Scholar

[27]

E. Massad, F. A. Coutinho, M. N. Burattini and L. F. Lopez, The risk of yellow fever in a dengue-infested area,, Transactions of the Royal Society of Tropical Medicine and Hygiene, 95 (2001), 370.  doi: 10.1016/S0035-9203(01)90184-1.  Google Scholar

[28]

D. T. Mourya, P. Yadav and A. C. Mishra, Effect of temperature stress on immature stages and susceptibility of Aedes aegypti mosquitoes to chikungunya virus,, American Journal Tropical Medicine and Hygiene, 70 (2004), 346.   Google Scholar

[29]

L. E. Muir and B. H. Kay, Aedes aegypti survival and dispersal estimated by mark-release-recapture in northern Australia,, American Journal of Tropical Medicine and Hygiene, 58 (1998), 277.   Google Scholar

[30]

M. Otero, H. G. Solari and N. Schweigmann, A stochastic population dynamics model for Aedes aegypti: Formulation and application to a city with temperate climate,, Bulletin of Mathematical Biology, 68 (2006), 1945.  doi: 10.1007/s11538-006-9067-y.  Google Scholar

[31]

C. Perret, K. Abarca, J. Ovalle, P. Ferrer, P. Godoy, A. Olea, X. Aguilera and M. Ferrés, Dengue-1 virus isolation during first dengue fever outbreak on Easter Island, Chile,, Emerg Infect Dis., 9 (2003), 1465.  doi: 10.3201/eid0911.020788.  Google Scholar

[32]

R. Ross, "The Prevention of Malaria,", John Murray, (1910).   Google Scholar

[33]

G. W. Schultz, Seasonal abundance of dengue vectors in Manila, Republic of the Philippines,, Southeast Asian Journal of Tropical Medicine and Public Health, 24 (1993), 369.   Google Scholar

[34]

D. L. Smith, J. Dushoff and F. E. Mckenzie, The risk of a mosquito-borne infection in a heterogeneous environment,, PLoS Biology, 2 (2004), 1957.   Google Scholar

[35]

S. T. Stoddard, A. C. Morrison, G. M. Vazquez-Prokopec, V. Paz Soldan, T. J. Kochel, U. Kitron, J. P. Elder and T. W. Scott, The role of human movement in the transmission of vector-borne pathogens,, PLoS Negl. Trop. Dis., 3 (2009).  doi: 10.1371/journal.pntd.0000481.  Google Scholar

[36]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[37]

D. W. Vaughn, S. Green, S. Kalayanarooj, B. L. Innis, S. Nimmannitya, S. Suntayakorn, T. P. Endy, B. Raengsakulrach, A. L. Rothman, F. A. Ennis and A. Nisalak, Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity,, Journal of Infectious Diseases, 181 (2000), 2.  doi: 10.1086/315215.  Google Scholar

[38]

H. J. Wearing, P. Rohani and M. J. Keeling, Appropriate models for the management of infectious diseases,, PLoS Medicine, 2 (2005).  doi: 10.1371/journal.pmed.0020174.  Google Scholar

[39]

World Health Organization, Dengue and dengue hemorrhagic fever, accessed March 04, 2006., Available from: , ().   Google Scholar

[40]

World Health Organization, Clinical diagnosis of dengue, accessed April 04, 2006., Available from: , (): 012.   Google Scholar

show all references

References:
[1]

X. Aguilera, A. Olea, J. Mora, K. Abarca and J. Segovia, Brote de dengue en Isla de Pascua,, El Vigia (Boletín de Vigilancia en Salud Püblica), 16 (2002), 37.   Google Scholar

[2]

R. M. Anderson and R. M. May, "Infectious Diseases of Humans,", Oxford University Press, (1991).  doi: 10.1016/0046-8177(90)90224-S.  Google Scholar

[3]

F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer-Verlag, (2000).  doi: 10.1007/978-1-4614-1686-9.  Google Scholar

[4]

G. Chowell, B. Cazelles, H. Broutin and C. V. Munayco, The influence of climatic and geographic factors on the timing of dengue epidemics in Peru, 1994-2008,, BMC Infectious Diseases, 11 (2011).  doi: 10.1186/1471-2334-11-164.  Google Scholar

[5]

G. Chowell, P. Diaz-Duenas, J. C. Miller, P. W. Fenimore, J. M. Hyman and C. Castillo-Chavez, Estimation of the reproduction number of dengue fever from spatial epidemic data,, Mathematical Biosciences, 208 (2007), 571.  doi: 10.1016/j.mbs.2006.11.011.  Google Scholar

[6]

G. Chowell, C. A. Torre, C. Munyaco-Escate, L. Suarez -Ognio, R. Lopez-Cruz, J. M. Hyman and C. Castillo-Chavez, Spatial and temporal dynamics of dengue fever in Peru: 1994-2006,, Epidemiology and Infection, 8 (2008), 1.  doi: 10.1017/S0950268808000290.  Google Scholar

[7]

G. Chowell and F. Sanchez, Climate-based descriptive models of dengue fever: The 2002 epidemic in Colima, Mexico,, Journal of Environmental Health, 68 (2006), 40.   Google Scholar

[8]

O. Diekmann and J. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation,", Wiley Series in Mathematical and Computational Biology, (2000).   Google Scholar

[9]

, Dirección Meteorológica de Chile., Available from: , ().   Google Scholar

[10]

C. Favier, N. Degallier, M. G. Rosa-Freitas, J. P. Boulanger, J. R. Costa Lima, J. F. Luitgards-Moura, C. E. Menkes, B. Mondet, C. Oliveira, E. T. Weimann and P. Tsouris, Early determination of the reproduction number for vector-borne diseases: The case of dengue in Brazil,, Tropical Medicine and International Health, 11 (2006), 332.  doi: 10.1111/j.1365-3156.2006.01560.x.  Google Scholar

[11]

N. M. Ferguson, C. A. Donnelly and R. M. Anderson, Transmission dynamics and epidemiology of dengue: Insights from age-stratified sero-prevalence surveys,, Phil. Trans. Roy. Soc. Lond. B, 354 (1999), 757.  doi: 10.1098/rstb.1999.0428.  Google Scholar

[12]

D. A. Focks, E. Daniels, D. G. Haile and J. E. Keesling, A simulation model of the epidemiology of urban dengue fever: Literature analysis, model development, preliminary validation, and samples of simulation results,, American Journal of Tropical Medicine and Hygiene, 53 (1995), 489.   Google Scholar

[13]

D. J. Gubler, Dengue and dengue hemorrhagic fever,, Clinical Microbiology Reviews, 11 (1998), 480.   Google Scholar

[14]

L. Gustafsson and M. Sternad, Bringing consistency to simulation of population models-Poisson simulation as a bridge between micro and macro simulation,, Mathematical Biosciences, 209 (2007), 361.  doi: 10.1016/j.mbs.2007.02.004.  Google Scholar

[15]

S. B. Halstead, Dengue virus-mosquito interactions,, Annu Rev Entomol., 53 (2007), 273.  doi: 10.1146/annurev.ento.53.103106.093326.  Google Scholar

[16]

Y. H. Hsieh and C. W. Chen, Turning points, reproduction number, and impact of climatological events for multi-wave dengue outbreaks,, Trop. Med. Int. Health., 14 (2009), 628.  doi: 10.1111/j.1365-3156.2009.02277.x.  Google Scholar

[17]

Y. H. Hsieh and S. Ma, Intervention measures, turning point, and reproduction number for dengue, Singapore, 2005,, American Journal of Tropical Medicine and Hygiene, 80 (2009), 66.   Google Scholar

[18]

J. M. Hyman, J. Li and E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV,, Mathematical Biosciences, 155 (1999), 77.  doi: 10.1016/S0025-5564(98)10057-3.  Google Scholar

[19]

Instituto Nacional de Estadísticas (INE), Estadísticas Demográficas y Vitales, 2009., Available from: , ().   Google Scholar

[20]

J. A. Jacquez, "Compartmental Analysis in Biology and Medicine,", Michigan Thompson-Shore, (1996).   Google Scholar

[21]

T. H. Jetten and D. A. Focks, Potential changes in the distribution of dengue transmission under climate warming,, American Journal Tropical Medicine and Hygiene, 57 (1997), 285.   Google Scholar

[22]

J. S. Koopman, D. R. Prevots, M. A. Vaca Marin, H. Gomez Dantes, M. L. Zarate Aquino, I. M. Longini, Jr and J. Sepulveda Amor, Determinants and predictors of dengue infection in Mexico., American Journal of Epidemiology, 133 (1991), 1168.   Google Scholar

[23]

C. F. Li, T. W. Lim, L. L. Han and R. Fang, Rainfall, abundance of Aedes aegypti and dengue infection in Selangor, Malaysia,, Southeast Asian Journal of Tropical Medicine and Public Health, 16 (1985), 560.   Google Scholar

[24]

P. M. Luz, C. T. Codeco, E. Massad and C. J. Struchiner, Uncertainties regarding dengue modeling in Río de Janeiro, Brazil,, Memórias do Instituto Oswaldo Cruz, 98 (2003), 871.  doi: 10.1590/S0074-02762003000700002.  Google Scholar

[25]

G. MacDonald, "The Epidemiology and Control of Malaria,", Chapter Epidemics, (1957), 45.   Google Scholar

[26]

C. A. Marques, O. P. Forattini and E. Massad, The basic reproduction number for dengue fever in São Paulo state, Brazil: 1990-1991 epidemic,, Transactions of the Royal Society of Tropical Medicine and Hygiene, 88 (1994), 58.   Google Scholar

[27]

E. Massad, F. A. Coutinho, M. N. Burattini and L. F. Lopez, The risk of yellow fever in a dengue-infested area,, Transactions of the Royal Society of Tropical Medicine and Hygiene, 95 (2001), 370.  doi: 10.1016/S0035-9203(01)90184-1.  Google Scholar

[28]

D. T. Mourya, P. Yadav and A. C. Mishra, Effect of temperature stress on immature stages and susceptibility of Aedes aegypti mosquitoes to chikungunya virus,, American Journal Tropical Medicine and Hygiene, 70 (2004), 346.   Google Scholar

[29]

L. E. Muir and B. H. Kay, Aedes aegypti survival and dispersal estimated by mark-release-recapture in northern Australia,, American Journal of Tropical Medicine and Hygiene, 58 (1998), 277.   Google Scholar

[30]

M. Otero, H. G. Solari and N. Schweigmann, A stochastic population dynamics model for Aedes aegypti: Formulation and application to a city with temperate climate,, Bulletin of Mathematical Biology, 68 (2006), 1945.  doi: 10.1007/s11538-006-9067-y.  Google Scholar

[31]

C. Perret, K. Abarca, J. Ovalle, P. Ferrer, P. Godoy, A. Olea, X. Aguilera and M. Ferrés, Dengue-1 virus isolation during first dengue fever outbreak on Easter Island, Chile,, Emerg Infect Dis., 9 (2003), 1465.  doi: 10.3201/eid0911.020788.  Google Scholar

[32]

R. Ross, "The Prevention of Malaria,", John Murray, (1910).   Google Scholar

[33]

G. W. Schultz, Seasonal abundance of dengue vectors in Manila, Republic of the Philippines,, Southeast Asian Journal of Tropical Medicine and Public Health, 24 (1993), 369.   Google Scholar

[34]

D. L. Smith, J. Dushoff and F. E. Mckenzie, The risk of a mosquito-borne infection in a heterogeneous environment,, PLoS Biology, 2 (2004), 1957.   Google Scholar

[35]

S. T. Stoddard, A. C. Morrison, G. M. Vazquez-Prokopec, V. Paz Soldan, T. J. Kochel, U. Kitron, J. P. Elder and T. W. Scott, The role of human movement in the transmission of vector-borne pathogens,, PLoS Negl. Trop. Dis., 3 (2009).  doi: 10.1371/journal.pntd.0000481.  Google Scholar

[36]

P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission,, Mathematical Biosciences, 180 (2002), 29.  doi: 10.1016/S0025-5564(02)00108-6.  Google Scholar

[37]

D. W. Vaughn, S. Green, S. Kalayanarooj, B. L. Innis, S. Nimmannitya, S. Suntayakorn, T. P. Endy, B. Raengsakulrach, A. L. Rothman, F. A. Ennis and A. Nisalak, Dengue viremia titer, antibody response pattern, and virus serotype correlate with disease severity,, Journal of Infectious Diseases, 181 (2000), 2.  doi: 10.1086/315215.  Google Scholar

[38]

H. J. Wearing, P. Rohani and M. J. Keeling, Appropriate models for the management of infectious diseases,, PLoS Medicine, 2 (2005).  doi: 10.1371/journal.pmed.0020174.  Google Scholar

[39]

World Health Organization, Dengue and dengue hemorrhagic fever, accessed March 04, 2006., Available from: , ().   Google Scholar

[40]

World Health Organization, Clinical diagnosis of dengue, accessed April 04, 2006., Available from: , (): 012.   Google Scholar

[1]

Yancong Xu, Lijun Wei, Xiaoyu Jiang, Zirui Zhu. Complex dynamics of a SIRS epidemic model with the influence of hospital bed number. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021016

[2]

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

[3]

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

[4]

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

[5]

Rong Wang, Yihong Du. Long-time dynamics of a diffusive epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020360

[6]

Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159

[7]

Yoichi Enatsu, Emiko Ishiwata, Takeo Ushijima. Traveling wave solution for a diffusive simple epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 835-850. doi: 10.3934/dcdss.2020387

[8]

Yi-Long Luo, Yangjun Ma. Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 921-966. doi: 10.3934/dcds.2020304

[9]

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

[10]

Martin Kalousek, Joshua Kortum, Anja Schlömerkemper. Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 17-39. doi: 10.3934/dcdss.2020331

[11]

Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118

[12]

Xin Zhao, Tao Feng, Liang Wang, Zhipeng Qiu. Threshold dynamics and sensitivity analysis of a stochastic semi-Markov switched SIRS epidemic model with nonlinear incidence and vaccination. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021010

[13]

Attila Dénes, Gergely Röst. Single species population dynamics in seasonal environment with short reproduction period. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020288

[14]

Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251

[15]

Philippe G. Ciarlet, Liliana Gratie, Cristinel Mardare. Intrinsic methods in elasticity: a mathematical survey. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 133-164. doi: 10.3934/dcds.2009.23.133

[16]

Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020446

[17]

Urszula Ledzewicz, Heinz Schättler. On the role of pharmacometrics in mathematical models for cancer treatments. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 483-499. doi: 10.3934/dcdsb.2020213

[18]

Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276

[19]

Juntao Sun, Tsung-fang Wu. The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function. Discrete & Continuous Dynamical Systems - A, 2021  doi: 10.3934/dcds.2021011

[20]

Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari. Mathematical analysis of a three-tiered food-web in the chemostat. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020369

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (92)
  • HTML views (0)
  • Cited by (11)

[Back to Top]