How macroscopic laws describe complex dynamics: asymptomatic population and CoviD-19 spreading
TL;DR: A system of coupled differential equations is studied which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation and shows the equivalence of the two methods.
Abstract: Macroscopic growth laws, solutions of mean field equations, describe in an effective way an underlying complex dynamics. They are applied to study the spreading of infections, as in the case of CoviD-19, where the counting of the cumulated number $N(t)$ of detected infected individuals is a generally accepted, coarse-grain, variable to understand the epidemic phase. However $N(t)$ does not take into account the unknown number of asymptomatic, not detected, cases $A(t)$. Therefore, the question arises if the observed time series of data of $N(t)$ is a reliable tool for monitoring the evolution of the infectious disease. We study a system of coupled differential equations which includes the dynamics of the spreading among symptomatic and asymptomatic individuals and the strong containment effects due to the social isolation. The solution is therefore compared with a macroscopic law for the population $N(t)$ coming from a single, non-linear, differential equation with no explicit reference to $A(t)$, showing the equivalence of the two methods. Indeed, $N(t)$ takes into account a more complex and detailed population dynamics which permits the evaluation of the number of asymptomatic individuals also. The model is then applied to Covid-19 spreading in Italy where a transition from an exponential behavior to a Gompertz growth for $N(t)$ has been observed in more recent data. Then the information contained in the data analysis of $N(t)$ is reliable to understand the epidemic phase, although it does not describe the total infected population. The asymptomatic population is larger than the symptomatic one in the fast growth phase of the spreading.
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TL;DR: In this article, a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters, is investigated under self-mapping properties, and the periodicity of the solution is examined by using integral control and optimal control is discussed in the sequel.
Abstract: Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.
5 citations
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TL;DR: The frequent opportunities I have had of receiving pleasure from your writings and conversation, have induced me to prefer offering to the Royal Society through your medium, this Paper on Life Contingencies, which forms part of a continuation of my original paper on the same subject, published among the valuable papers of the Society, as by passing through your hands it may receive the advantage of your judgment.
Abstract: Dear Sir, The frequent opportunities I have had of receiving pleasure from your writings and conversation, have induced me to prefer offering to the Royal Society through your medium, this Paper on Life Contingencies, which forms part of a continuation of my original paper on the same subject, published among the valuable papers of the Society, as by passing through your hands it may receive the advantage of your judgment.
3,257 citations
TL;DR: This review will help understand the biology and potential risk of CoVs that exist in richness in wildlife such as bats and describe diseases caused by different CoVs in humans and animals.
Abstract: The recent emergence of a novel coronavirus (2019-nCoV), which is causing an outbreak of unusual viral pneumonia in patients in Wuhan, a central city in China, is another warning of the risk of CoVs posed to public health. In this minireview, we provide a brief introduction of the general features of CoVs and describe diseases caused by different CoVs in humans and animals. This review will help understand the biology and potential risk of CoVs that exist in richness in wildlife such as bats.
2,480 citations
Additional excerpts
...Various growth patterns have been very recently applied to the time evolution of the CoviD-19 infection [7] [8] [9] [10] [11] [12] [13] ....
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...(7, 8) , which shows that the time evolution of N (t) anticipates the other by about 8 days....
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TL;DR: COVID-19 cases in the United States that occurred during February 12-March 16, 2020 and severity of disease (hospitalization, admission to intensive care unit [ICU], and death) were analyzed by age group, suggesting that the risk for serious disease and death from CO VID-19 is higher in older age groups.
Abstract: Globally, approximately 170,000 confirmed cases of coronavirus disease 2019 (COVID-19) caused by the 2019 novel coronavirus (SARS-CoV-2) have been reported, including an estimated 7,000 deaths in approximately 150 countries (1). On March 11, 2020, the World Health Organization declared the COVID-19 outbreak a pandemic (2). Data from China have indicated that older adults, particularly those with serious underlying health conditions, are at higher risk for severe COVID-19-associated illness and death than are younger persons (3). Although the majority of reported COVID-19 cases in China were mild (81%), approximately 80% of deaths occurred among adults aged ≥60 years; only one (0.1%) death occurred in a person aged ≤19 years (3). In this report, COVID-19 cases in the United States that occurred during February 12-March 16, 2020 and severity of disease (hospitalization, admission to intensive care unit [ICU], and death) were analyzed by age group. As of March 16, a total of 4,226 COVID-19 cases in the United States had been reported to CDC, with multiple cases reported among older adults living in long-term care facilities (4). Overall, 31% of cases, 45% of hospitalizations, 53% of ICU admissions, and 80% of deaths associated with COVID-19 were among adults aged ≥65 years with the highest percentage of severe outcomes among persons aged ≥85 years. In contrast, no ICU admissions or deaths were reported among persons aged ≤19 years. Similar to reports from other countries, this finding suggests that the risk for serious disease and death from COVID-19 is higher in older age groups.
1,896 citations
Journal Article•
TL;DR: The assumption of uniform nascent growth is not supported by theory or data, and individual cancers have not been shown to follow the complex growth curves predicted by the Speer model, so an alternative Gompertzian model is suggested which is parsimonious and has many other intuitive and empirical advantages.
Abstract: The pattern of growth of human breast cancer is important theoretically and clinically. Speer et al. (Cancer Res., 44: 4124–4130, 1984) have recently proposed that all individual tumors initially grow with identical Gompertzian parameters, but subsequently develop kinetic heterogeneity by a random time-dependent process. This concept has elicited interest because it fits clinical data for the survival of untreated patients, for the progression of shadows on serial paired mammograms, and for time-to-relapse following mastectomy. The success of these curve-fits is compelling, and the model has been applied to clinical trials. However, the assumption of uniform nascent growth is not supported by theory or data, and individual cancers have not been shown to follow the complex growth curves predicted by the Speer model. As an alternative, if kinetic heterogeneity is understood to be an intrinsic property of neoplasia, the same three historical data sets are fit well by an unadorned Gompertzian model which is parsimonious and has many other intuitive and empirical advantages. The two models differ significantly in such clinical projections as the estimated duration of silent growth prior to diagnosis and the anticipated optimal chemotherapy schedule postsurgery.
672 citations