A comprehensive spatial-temporal infection model

Ramaswamy, Harisankar; Oberai, Assad A.; Yortsos, Y.C.

doi:10.1016/j.ces.2020.116347

Cited by 14 publications

(39 citation statements)

References 24 publications

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“…Also, Roosa et al [18,19] investigated phenomenological models to perform real-time and short-term predictions of the reported cases for the Covid-19 pandemic in China. Most of these models depend only on the time variable t , but in [20], where a useful analogy is presented between the spreading of an infection and the process of chemical reaction, the dependence of a space variable of the spread of infection is also taken into consideration. In [21], a novel approach is presented for reducing the cost of testing without compromising accuracy: combining subsamples and testing them in groups.…”

Section: Discussionmentioning

confidence: 99%

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period

2021

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In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed.

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Section: Discussionmentioning

confidence: 99%

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period

2021

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“…where I 0 (t) can be obtained from Equations ( 27) and (28). An illustrative example is shown in Figure 13.…”

Section: Effect Of Lockdowns Inside a Random Tree With Healingsmentioning

confidence: 99%

“…It has been studied extensively also in the realm of statistical physics of disordered systems (e.g., [17][18][19]). More recently, a great deal of interest has been devoted to the study and development of new scenarios to describe COVID-19 spreading [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In addition, we can mention that a lot of attention has been drawn to population structures displaying complex and heterogeneous connectivity patterns, as well as to the associated dynamics of epidemic and infection spreading processes in the so-called metapopulation models [36,37].…”

Section: Introductionmentioning

confidence: 99%

Spreading of Infections on Network Models: Percolation Clusters and Random Trees

Roman

Croccolo

2021

Mathematics

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We discuss network models as a general and suitable framework for describing the spreading of an infectious disease within a population. We discuss two types of finite random structures as building blocks of the network, one based on percolation concepts and the second one on random tree structures. We study, as is done for the SIR model, the time evolution of the number of susceptible (S), infected (I) and recovered (R) individuals, in the presence of a spreading infectious disease, by incorporating a healing mechanism for infecteds. In addition, we discuss in detail the implementation of lockdowns and how to simulate them. For percolation clusters, we present numerical results based on site percolation on a square lattice, while for random trees we derive new analytical results, which are illustrated in detail with a few examples. It is argued that such hierarchical networks can complement the well-known SIR model in most circumstances. We illustrate these ideas by revisiting USA COVID-19 data.

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“…Diffusion can produce traveling waves, the existence of which has been proved rigorously in [6,15,24,[28][29][30][31]. In 2021, Ramaswamy, Oberai and Yortsos [18] proposed a comprehensive temporal-spatial infection model that takes into consideration the influence of advection on the spread of the infectious disease in addition to diffusion.…”

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confidence: 99%

“…We assume that the total population density is constant in space and time for simplicity, which is also approximately true in the time frame of infectious diseases spreading. We use S(x, t), I(x, t) and R(x, t) to denote the fractions of susceptible, infected, and recovered individuals at space x and time t. This paper is concerned with numerical methods for the following advection-diffusion-reaction equations [18] ∂S ∂t + u • ∇S − ∇ • D∇S = −βSI, (1.1a)…”

mentioning

confidence: 99%

A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

Kou¹,

Chen²,

Wang³

et al. 2023

CPAA

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In this paper, we propose an efficient numerical method for a comprehensive infection model that is formulated by a system of nonlinear coupling advection-diffusion-reaction equations. Using some subtle mixed explicitimplicit treatments, we construct a linearized and decoupled discrete scheme. Moreover, the proposed scheme is capable of preserving the positivity of variables, which is an essential requirement of the model under consideration. The proposed scheme uses the cell-centered finite difference method for the spatial discretization, and thus, it is easy to implement. The diffusion terms are treated implicitly to improve the robustness of the scheme. A semi-implicit upwind approach is proposed to discretize the advection terms, and a distinctive feature of the resulting scheme is to preserve the positivity of variables without any restriction on the spatial mesh size and time step size. We rigorously prove the unique existence of discrete solutions and positivity-preserving property of the proposed scheme without requirements for the mesh size and time step size. It is worthwhile to note that these properties are proved using the discrete variational principles rather than the conventional approaches of matrix analysis. Numerical results are also provided to assess the performance of the proposed scheme.

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A comprehensive spatial-temporal infection model

Cited by 14 publications

References 24 publications

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period

Spreading of Infections on Network Models: Percolation Clusters and Random Trees

A linear, decoupled and positivity-preserving numerical scheme for an epidemic model with advection and diffusion

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