
Previous Article
Chaotic spreading of epidemics in complex networks of excitable units
 MBE Home
 This Issue

Next Article
Critical role of nosocomial transmission in the Toronto SARS outbreak
Modeling and optimal regulation of erythropoiesis subject to benzene intoxication
1.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 276958212 
2.  Department of Mathematics and Computer Science, Meredith College, Raleigh, NC 27607, United States 
3.  CIIT Centers for Health Research, Research Triangle Park, NC 27709, United States 
4.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, United States 
Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis (blood cell production and development). An agestructured model was used to examine the process of erythropoiesis, the development of red blood cells. This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations. In addition, we formulated an optimal control problem for the control of erythropoiesis and performed numerical simulations to compare the performance of the optimal feedback law and another feedback function based on the Hill function.
[1] 
Hassan Tahir, Asaf Khan, Anwarud Din, Amir Khan, Gul Zaman. Optimal control strategy for an agestructured SIR endemic model. Discrete & Continuous Dynamical Systems  S, 2021, 14 (7) : 25352555. doi: 10.3934/dcdss.2021054 
[2] 
HeeDae Kwon, Jeehyun Lee, Myoungho Yoon. An agestructured model with immune response of HIV infection: Modeling and optimal control approach. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 153172. doi: 10.3934/dcdsb.2014.19.153 
[3] 
Z.R. He, M.S. Wang, Z.E. Ma. Optimal birth control problems for nonlinear agestructured population dynamics. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 589594. doi: 10.3934/dcdsb.2004.4.589 
[4] 
Zhihua Liu, Yayun Wu, Xiangming Zhang. Existence of periodic wave trains for an agestructured model with diffusion. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2021009 
[5] 
Jianxin Yang, Zhipeng Qiu, XueZhi Li. Global stability of an agestructured cholera model. Mathematical Biosciences & Engineering, 2014, 11 (3) : 641665. doi: 10.3934/mbe.2014.11.641 
[6] 
Ryszard Rudnicki, Radosław Wieczorek. On a nonlinear agestructured model of semelparous species. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 26412656. doi: 10.3934/dcdsb.2014.19.2641 
[7] 
Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an agestructured model with relapse. Discrete & Continuous Dynamical Systems  B, 2020, 25 (6) : 22452270. doi: 10.3934/dcdsb.2019226 
[8] 
Sebastian Aniţa, AnaMaria Moşsneagu. Optimal harvesting for agestructured population dynamics with sizedependent control. Mathematical Control & Related Fields, 2019, 9 (4) : 607621. doi: 10.3934/mcrf.2019043 
[9] 
Folashade B. Agusto. Optimal control and costeffectiveness analysis of a three agestructured transmission dynamics of chikungunya virus. Discrete & Continuous Dynamical Systems  B, 2017, 22 (3) : 687715. doi: 10.3934/dcdsb.2017034 
[10] 
Geni Gupur, XueZhi Li. Global stability of an agestructured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 643652. doi: 10.3934/dcdsb.2004.4.643 
[11] 
Shengqin Xu, Chuncheng Wang, Dejun Fan. Stability and bifurcation in an agestructured model with stocking rate and time delays. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 25352549. doi: 10.3934/dcdsb.2018264 
[12] 
Linlin Li, Bedreddine Ainseba. Largetime behavior of matured population in an agestructured model. Discrete & Continuous Dynamical Systems  B, 2021, 26 (5) : 25612580. doi: 10.3934/dcdsb.2020195 
[13] 
Georgi Kapitanov, Christina Alvey, Katia VogtGeisse, Zhilan Feng. An agestructured model for the coupled dynamics of HIV and HSV2. Mathematical Biosciences & Engineering, 2015, 12 (4) : 803840. doi: 10.3934/mbe.2015.12.803 
[14] 
Cameron J. Browne, Sergei S. Pilyugin. Global analysis of agestructured withinhost virus model. Discrete & Continuous Dynamical Systems  B, 2013, 18 (8) : 19992017. doi: 10.3934/dcdsb.2013.18.1999 
[15] 
Hao Kang, Qimin Huang, Shigui Ruan. Periodic solutions of an agestructured epidemic model with periodic infection rate. Communications on Pure & Applied Analysis, 2020, 19 (10) : 49554972. doi: 10.3934/cpaa.2020220 
[16] 
Xichao Duan, Sanling Yuan, Kaifa Wang. Dynamics of a diffusive agestructured HBV model with saturating incidence. Mathematical Biosciences & Engineering, 2016, 13 (5) : 935968. doi: 10.3934/mbe.2016024 
[17] 
Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear agestructured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337354. doi: 10.3934/mbe.2008.5.337 
[18] 
Georgi Kapitanov. A double agestructured model of the coinfection of tuberculosis and HIV. Mathematical Biosciences & Engineering, 2015, 12 (1) : 2340. doi: 10.3934/mbe.2015.12.23 
[19] 
Hisashi Inaba. Mathematical analysis of an agestructured SIR epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 6996. doi: 10.3934/dcdsb.2006.6.69 
[20] 
Hossein Mohebbi, Azim Aminataei, Cameron J. Browne, Mohammad Reza Razvan. Hopf bifurcation of an agestructured virus infection model. Discrete & Continuous Dynamical Systems  B, 2018, 23 (2) : 861885. doi: 10.3934/dcdsb.2018046 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]