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

The basic reproductive ratio, R0, is defined as the expected number of secondary infections arising from a single individual during his or her entire infectious period, in a population of susceptibles. This concept is fundamental to the study of epidemiology and within-host pathogen dynamics. Most importantly, R0 often serves as a threshold parameter that predicts whether an infection will spread. Related parameters which share this threshold behaviour, however, may or may not give the true value of R0. In this paper we give a brief overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models. We also review common means of estimating R0 from epidemiological data. Finally, we survey the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus.

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Perspectives on the basic reproductive ratio

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

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling

There is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a media-fueled rush to vaccination; conversely, seasonal diseases may receive little media attention, despite their high mortality rate, due to their perceived lack of newness. We formulate a deterministic transmission and vaccination model to investigate the effects of media coverage on the transmission dynamics of influenza. The population is subdivided into different classes according to their disease status. The compartmental model includes the effect of media coverage on reporting the number of infections as well as the number of individuals successfully vaccinated. A threshold parameter (the basic reproductive ratio) is analytically derived and used to discuss the local stability of the disease-free steady state. The impact of costs that can be incurred, which include vaccination, education, implementation and campaigns on media coverage, are also investigated using optimal control theory. A simplified version of the model with pulse vaccination shows that the media can trigger a vaccinating panic if the vaccine is imperfect and simplified messages result in the vaccinated mixing with the infectives without regard to disease risk. The effects of media on an outbreak are complex. Simplified understandings of disease epidemiology, propogated through media soundbites, may make the disease significantly worse.

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The impact of media coverage on the transmission dynamics of human influenza.

The basic reproductive ratio, 𝑅0, is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if 𝑅0l1, the disease dies out, whereas if 𝑅0g1, the disease persists. 𝑅0 has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, 𝑅0 is flawed. Diseases can persist with 𝑅0l1, while diseases with 𝑅0g1 can die out. We show that the same model of malaria gives many different values of 𝑅0, depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of 𝑅0 for a variety of diseases, and examine some of the alternatives that have been proposed. If 𝑅0 is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.

Robert J. Smith

Papers

Perspectives on the basic reproductive ratio

Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling

The impact of media coverage on the transmission dynamics of human influenza.

The failure of R0.

The Failure of R 0