•Journal•ISSN: 1547-1063
Mathematical Biosciences and Engineering
Arizona State University
About: Mathematical Biosciences and Engineering is an academic journal published by Arizona State University. The journal publishes majorly in the area(s): Medicine & Computer science. It has an ISSN identifier of 1547-1063. It is also open access. Over the lifetime, 3415 publications have been published receiving 31566 citations. The journal is also known as: MBE.
Topics: Medicine, Computer science, Population, Biology, Engineering
Papers published on a yearly basis
Papers
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TL;DR: Questions addressed by these models mainly concentrate on TB control strategies, optimal vaccination policies, approaches toward the elimination of TB in the U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses of the immune system, impacts of demography, the role of public transportation systems, and the impact of contact patterns.
Abstract: The reemergence of tuberculosis (TB) from the 1980s to the early
1990s instigated extensive researches on the mechanisms behind the
transmission dynamics of TB epidemics. This article provides a
detailed review of the work on the dynamics and control of TB. The
earliest mathematical models describing the TB dynamics appeared in
the 1960s and focused on the prediction and control strategies using
simulation approaches. Most recently developed models not only pay
attention to simulations but also take care of dynamical analysis
using modern knowledge of dynamical systems. Questions addressed by
these models mainly concentrate on TB control strategies, optimal
vaccination policies, approaches toward the elimination of TB in the
U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses
of the immune system, impacts of demography, the role of public
transportation systems, and the impact of contact patterns. Model
formulations involve a variety of mathematical areas, such as ODEs
(Ordinary Differential Equations) (both autonomous and
non-autonomous systems), PDEs (Partial Differential Equations),
system of difference equations, system of integro-differential
equations, Markov chain model, and simulation models.
1,327 citations
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TL;DR: Analytical and numerical results indicate that the coronavirus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.
Abstract: We propose a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) in Wuhan, China. Our model describes the multiple transmission pathways in the infection dynamics, and emphasizes the role of the environmental reservoir in the transmission and spread of this disease. Our model also employs non-constant transmission rates which change with the epidemiological status and environmental conditions and which reflect the impact of the on-going disease control measures. We conduct a detailed analysis of this model, and demonstrate its application using publicly reported data. Among other findings, our analytical and numerical results indicate that the coronavirus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.
340 citations
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TL;DR: Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form betaI(p)S(q) for the case p = 1 are constructed and global stability of the models is established.
Abstract: Explicit Lyapunov functions for SIR and SEIR compartmental
epidemic models with nonlinear incidence of the form $\beta I^p S^q$
for the case $p \leq 1$
are constructed. Global stability of the models is thereby established.
260 citations
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TL;DR: A dynamic mathematical model is formulated that describes the interaction of the immune system with the human immunodeficiency virus and that permits drug "cocktail" therapies and supports a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
Abstract: We formulate a dynamic mathematical model that describes the
interaction of the immune system with the human immunodeficiency
virus (HIV) and that permits drug ''cocktail'' therapies. We
derive HIV therapeutic strategies by formulating and analyzing an
optimal control problem using two types of dynamic treatments
representing reverse transcriptase (RT) inhibitors and protease
inhibitors (PIs). Continuous optimal therapies are found by
solving the corresponding optimality systems. In addition, using
ideas from dynamic programming, we formulate and derive suboptimal
structured treatment interruptions (STI) in antiviral therapy that
include drug-free periods of immune-mediated control of HIV. Our
numerical results support a scenario in which STI therapies can
lead to long-term control of HIV by the immune response system
after discontinuation of therapy.
230 citations
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TL;DR: Optimal control theory is applied to suggest the most effective mitigation strategy to minimize the number of individuals who become infected in the course of an infection while efficiently balancing vaccination and treatment applied to the models with various cost scenarios.
Abstract: Mathematical models provide a powerful tool for investigating the
dynamics and control of infectious diseases, but quantifying the
underlying epidemic structure can be challenging especially for new
and under-studied diseases.
Variations of standard SIR, SIRS, and SEIR epidemiological
models are considered to determine the sensitivity of these models to
various parameter values that may not be fully known when the models are
used to investigate emerging diseases. Optimal control theory is applied
to suggest the most effective mitigation
strategy to minimize the number of individuals who become infected in the
course of an infection while efficiently balancing
vaccination and treatment applied to the models with various cost
scenarios. The optimal control simulations suggest that regardless of the
particular epidemiological structure and of the comparative cost of
mitigation strategies, vaccination, if available, would be a
crucial piece of any intervention plan.
195 citations