Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

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Differential Equations and Dynamical Systems

Importance Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes coronavirus disease 2019 (COVID-19) has reached a pandemic level. Coronaviruses are known to affect the cardiovascular system. We review the basics of coronaviruses, with a focus on COVID-19, along with their effects on the cardiovascular system. Observations Coronavirus disease 2019 can cause a viral pneumonia with additional extrapulmonary manifestations and complications. A large proportion of patients have underlying cardiovascular disease and/or cardiac risk factors. Factors associated with mortality include male sex, advanced age, and presence of comorbidities including hypertension, diabetes mellitus, cardiovascular diseases, and cerebrovascular diseases. Acute cardiac injury determined by elevated high-sensitivity troponin levels is commonly observed in severe cases and is strongly associated with mortality. Acute respiratory distress syndrome is also strongly associated with mortality. Conclusions and Relevance Coronavirus disease 2019 is associated with a high inflammatory burden that can induce vascular inflammation, myocarditis, and cardiac arrhythmias. Extensive efforts are underway to find specific vaccines and antivirals against SARS-CoV-2. Meanwhile, cardiovascular risk factors and conditions should be judiciously controlled per evidence-based guidelines.

https://jamanetwork.com/journals/jamacardiology/articlepdf/2763846/jamacardiology_madjid_2020_rv_200002.pdf

Potential Effects of Coronaviruses on the Cardiovascular System: A Review.

eMedicine创建于1996年，由近万名临床医师作为作者或编辑参与此临床医学知识库的建设，其中编辑均是来自美国哈佛、耶鲁、斯坦福、芝加哥、德克萨斯、加州大学等各分校医学院的教授或副教授。

eMedicine

Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases. A key variable in such models is the reproductive number R. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number.

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How generation intervals shape the relationship between growth rates and reproductive numbers.

생체의 모델링과 Simulation

Comparison of the bronchodilator effects of aerosol fenoterol and isoproterenol.

Pine wilt disease is a lethal tree disease caused by nematodes carried by pine sawyer beetles. Once affected, the trees are destroyed within a few months, resulting in significant environmental and economic losses. The role of asymptomatic carrier trees in the disease dynamics remains unclear. We developed a mathematical model to investigate the effect of asymptomatic carriers on the long-term outcome of the disease. We performed a stability and sensitivity analysis to identify key parameters and used optimal control to examine several intervention options. Our model shows that, with the application of suitable controls, the disease can be eliminated in the vector population and all tree populations except for asymptomatic carriers. Of the possible controls (tree injection, elimination of infected trees, insecticide spraying), we determined that elimination of infected trees is crucial. However, if the costs of insecticide spraying increase, it can be supplemented (although not replaced entirely) by tree injection, so long as some spraying is still undertaken.

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Modelling the dynamics of Pine Wilt Disease with asymptomatic carriers and optimal control.

Resistance to a postinfection HIV vaccine that stimulates cytotoxic T-lymphocytes (CTLs) depends on the relationship between the vaccine strength, the fitness cost of the mutant strain, and the rate of mutant escape. If the vaccine is strong enough, both strains of the virus should be controlled by administering the vaccine sufficiently often. However, if escape mutation to the vaccine occurs, then either the wild type or the mutant can outcompete the other strain. Imperfect adherence may result in the persistence of the mutant, while fluctuations in the vaccination time—even if no vaccines are missed—may result in the mutant outcompeting the wild type.

/pdf/modelling-mutation-to-a-cytotoxic-t-lymphocyte-hiv-vaccine-omp63s3s79.pdf

Modelling Mutation to a Cytotoxic T-lymphocyte HIV Vaccine

https://mysite.science.uottawa.ca/rsmith43/PIs.pdf

Resistance to protease inhibitors in a model of HIV-1 infection with impulsive drug effects.

https://www.mdpi.com/2076-393X/2/2/397/pdf

Robert J. Smith

Papers

Comparison of the bronchodilator effects of aerosol fenoterol and isoproterenol.

Modelling the dynamics of Pine Wilt Disease with asymptomatic carriers and optimal control.

Modelling Mutation to a Cytotoxic T-lymphocyte HIV Vaccine

Resistance to protease inhibitors in a model of HIV-1 infection with impulsive drug effects.

Identifying the Conditions Under Which Antibodies Protect Against Infection by Equine Infectious Anemia Virus