A mathematical model for Chagas disease with infection-age-dependent infectivity

Inaba, Hisashi; Sekine, H.

doi:10.1016/j.mbs.2004.02.004

Cited by 95 publications

(62 citation statements)

References 14 publications

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“…Our interest in this paper is vaccine production, and calculation of R 0 is not important in this context. Computation of R 0 could in principle, of course, be done for models such as ours (e.g., see [16]), but we do not pursue that here.…”

Section: Discussionmentioning

confidence: 99%

Modeling Shrimp Biomass and Viral Infection for Production of Biological Countermeasures

Banks¹,

Bokil²,

Hu³

et al. 2005

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In this paper we develop a mathematical model for the rapid production of large quantities of therapeutic and/or preventative countermeasures. We couple equations for biomass production with those for vaccine production in shrimp that have been infected with a recombinant viral vector expressing a foreign antigen. The model system entails both size and class-age structure.Key Words: Size/class-age structured population models, shrimp growth/viral progression dynamics, latently-acutely infected. Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Section: Discussionmentioning

confidence: 99%

Modeling Shrimp Biomass and Viral Infection for Production of Biological Countermeasures

Banks¹,

Bokil²,

Hu³

et al. 2005

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“…This assumption is reasonable in some diseases such as influenza, but it is unreasonable in some other diseases, such as AIDS 10,11 and Chagas disease. 12 Therefore, it is more realistic and interesting to consider age-dependent epidemic models than ordinary differential equation (ODE) models. For more background of age-structured models, we refer the readers to Refs.…”

Section: Di(t) Dt = β 1 S(t)i(t) + β 2 V (T)i(t) − γ 1 I(t) − µ 1 I(tmentioning

confidence: 99%

Global Dynamics of an Svir Epidemiological Model With Infection Age and Nonlinear Incidence

Wang

2017

J. Biol. Syst.

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In this paper, an SVIR epidemiological model with infection age (time elapsed since the infection) and nonlinear incidence is studied. In the model, in order to reflect the dependence of disease progress on the infection age, the infected individual is structured by the infection age, and transmission and removal rates are assumed to depend on the infection age. By analyzing corresponding characteristic equations, the local stability of each of steady states of the model is established. It is proved that the semi-flow generated by this system is asymptotically smooth, and if the basic reproduction number is greater than unity, the system is uniformly persistent. By using Lyapunov functional and LaSalle's invariance principle, the global dynamics of the model is investigated. It is shown that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable and hence the disease dies out; and if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable and the disease persists. Numerical simulations are carried out to illustrate the main analytic results.

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“…Usually, vectors are the main source of transmission of vector-borne disease among their hosts, but there are some cases which show that direct transmission of a disease is also possible [9].…”

Section: Introductionmentioning

confidence: 99%

Qualitative behavior of vector-borne disease model

Ozair¹,

Din²,

Hussain³

et al. 2016

J. Nonlinear Sci. Appl.

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We investigate some qualitative behavior of a vector-borne disease model. Specially, we study local as well as global asymptotic stability of both disease-free and endemic equilibria of the model under certain parametric conditions. Furthermore, global behavior of disease-free equilibrium is investigated by constructing Lyapunov function, while global behavior of endemic equilibrium is discussed through geometric approach. Numerical simulations are provided to illustrate the theoretical discussion.

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A mathematical model for Chagas disease with infection-age-dependent infectivity

Cited by 95 publications

References 14 publications

Modeling Shrimp Biomass and Viral Infection for Production of Biological Countermeasures

Modeling Shrimp Biomass and Viral Infection for Production of Biological Countermeasures

Global Dynamics of an Svir Epidemiological Model With Infection Age and Nonlinear Incidence

Qualitative behavior of vector-borne disease model

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