Optimal control for an age-structured model for the transmission of hepatitis B

被引：0
作者：
Ramses Djidjou Demasse
Jean-Jules Tewa
Samuel Bowong
Yves Emvudu
机构：
[1] University of Yaounde 1,Faculty of Science
[2] University of Yaounde 1,National Advanced School of Engineering
[3] University of Douala,Faculty of Science
[4] UMI 209 IRD&UPMC UMMISCO,The African Center of Excellence in Information and Communication Technologies (CETIC)
[5] LIRIMA,undefined
[6] Project Team GRIMCAPE,undefined
[7] University of Yaounde 1,undefined
来源：
Journal of Mathematical Biology | 2016年 / 73卷
关键词：
HBV; Age structure; Non-linear dynamical system ; Stability; Optimal control; 35Q92; 49J20; 35B35; 92D30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.
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页码：305 / 333
页数：28
相关论文
共 88 条
[1]  
Barbu V(1999)Optimal control of population dynamics J Optim Theory Appl 102 1-14
[2]  
Iannelli M(1994)Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example Int Stat Rev 2 229-243
[3]  
Blower SM(2010)Optimal control of the dynamics of tuberculosis Nonlinear Dyn 61 729-748
[4]  
Dowlatabadi H(2013)An age-structured within-host model for multistrain malaria infections SIAM J Appl Math 73 572-592
[5]  
Bowong S(1990)On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations J Math Biol 28 365-382
[6]  
Djidjou Demasse R(2008)Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems J Math Anal Appl 341 501-518
[7]  
Ducrot A(1993)The influence of age on the development of the hepatitis B carrier state Proc R Soc Lond B 253 197-201
[8]  
Diekmann O(1996)The transmission dynamics and control of hepatitis B virus in the Gambia Stat Med 15 2215-2233
[9]  
Heesterbeek JAP(1996)Vaccination against hepatitis B virus in highly endemic area: Waning vaccine-induced immunity and the need for booster doses Trans R Soc Trop Med Hyg 90 436-440
[10]  
Metz JAJ(2013)Optimal control using state-dependent Riccati equation of lost of sight in a tuberculosis model Comp Apll Math 32 191-210
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