scholarly journals Spatio-temporal modeling of COVID-19 epidemic

2021 ◽  
pp. 23-37
Author(s):  
V.L. Sokolovsky ◽  
◽  
G.B. Furman ◽  
D.A. Polyanskaya ◽  
E.G. Furman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Mass Vaccination ◽  
Reaction Diffusion Equations ◽  
Disease Spread ◽  
Correct Prediction ◽  
Model Parameters ◽  
Population Mobility ◽  
Personal Protection Equipment ◽  
Infected People ◽  
Spatio Temporal

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven distribution of population, changes in population mobility, and changes in frequency of contacts between susceptible and infected people due to quarantine. We applied obtained analytical and numerical solutions to analyze different stages in the epidemic as well as its wave-like development influenced by imposing and canceling quarantine limitations. To take into account ultimate rate at which the disease spreads and its incubation period (when an infected person is not a source of contagion), we suggest using equations similar to the Cattaneo-Vernotte one. The suggested model allows predicting where the front of morbidity spread is going to occur, that is, a moving frontier between areas where there are infected people and areas where they are absent. Use of such models provides an opportunity to introduce differential quarantine measures basing on more objective grounds. At the end of 2020 mass vaccination started in some countries. We estimated a necessary number of people that had to be vaccinated so that new waves of COVID-19 epidemic would be prevented; in our estimates, not less than 80% of the country population should be vaccinated. Correct prediction of epidemic development is becoming more and more vital at the moment due to new and more contagious COVID-19 virus strains occurring in England, South Africa, and some other countries. Our research results can be used for predicting spread of COVID-19 and other communicable diseases; they can make for taking the most efficient measures for successful control over epidemics.

scholarly journals Spatio-temporal modeling of COVID-19 epidemic

2021 ◽  
pp. 23-37
Author(s):  
V.L. Sokolovsky ◽  
◽  
G.B. Furman ◽  
D.A. Polyanskaya ◽  
E.G. Furman ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Mass Vaccination ◽  
Reaction Diffusion Equations ◽  
Disease Spread ◽  
Correct Prediction ◽  
Model Parameters ◽  
Population Mobility ◽  
Personal Protection Equipment ◽  
Infected People ◽  
Spatio Temporal

In autumn and winter 2020–2021 there was a growth in morbidity with COVID-19. Since there are no efficient medications and mass vaccination has only just begun, quarantine, limitations on travels and contacts between people as well as use of personal protection equipment (masks) still remain priority measures aimed at preventing the disease from spreading. In this work we have analyzed how the epidemic developed and what impacts quarantine measures exerted on the disease spread; to do that we applied various mathematical models. It was shown that simple models belonging to SIR-type (S means susceptible; I, infected; and R, recovered or removed from the infected group) allowed estimating certain model parameters such as morbidity and recovery coefficients that could be used in more complicated models. We examined spatio-temporal epidemiologic models based on finding solutions to non-stationary two-dimensional reaction-diffusion equations. Such models allow taking into account uneven distribution of population, changes in population mobility, and changes in frequency of contacts between susceptible and infected people due to quarantine. We applied obtained analytical and numerical solutions to analyze different stages in the epidemic as well as its wave-like development influenced by imposing and canceling quarantine limitations. To take into account ultimate rate at which the disease spreads and its incubation period (when an infected person is not a source of contagion), we suggest using equations similar to the Cattaneo-Vernotte one. The suggested model allows predicting where the front of morbidity spread is going to occur, that is, a moving frontier between areas where there are infected people and areas where they are absent. Use of such models provides an opportunity to introduce differential quarantine measures basing on more objective grounds. At the end of 2020 mass vaccination started in some countries. We estimated a necessary number of people that had to be vaccinated so that new waves of COVID-19 epidemic would be prevented; in our estimates, not less than 80% of the country population should be vaccinated. Correct prediction of epidemic development is becoming more and more vital at the moment due to new and more contagious COVID-19 virus strains occurring in England, South Africa, and some other countries. Our research results can be used for predicting spread of COVID-19 and other communicable diseases; they can make for taking the most efficient measures for successful control over epidemics.

Diffusion-driven instability in oscillating environments

1995 ◽  
Vol 6 (4) ◽  
pp. 355-372 ◽  
Author(s):  
Jonathan A. Sherratt
Keyword(s):  
Diffusion Coefficients ◽  
Numerical Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Model Parameters ◽  
Seasonal Fluctuations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Ecological Applications ◽  
Parameter Values

Diffusion-driven instability in systems of reaction-diffusion equations is a commonly used model for pattern formation in both embryology and ecology. In ecological applications, model parameters tend to oscillate in time, because of either daily or seasonal fluctuations in the environment. I investigate the effects of such fluctuations on diffusion-driven instability by considering analytically the possibility of Turing bifurcations when the parameter values (diffusion coefficients and kinetic parameters) oscillate in time between two sets of constant values, with a period that is either very short or very long compared to the time scale of the growth and predation kinetics. I show that oscillations in the kinetics can have quite different effects from oscillations in the dispersal terms. I also discuss the comparison between the solution forms predicted by linear theory and the numerical solutions of a simple nonlinear predator-prey model.

scholarly journals Modifying the network-based stochastic SEIR model to account for quarantine: an application to COVID-19

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Chris Groendyke ◽  
Adam Combs
Keyword(s):  
Network Model ◽  
Transmission Rate ◽  
Disease Spread ◽  
Contact Network ◽  
Model Parameters ◽  
Seir Model ◽  
Disease States ◽  
Potential Contact ◽  
The Mean ◽  
Infectious State

Abstract Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

scholarly journals A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed A. Aba Oud ◽  
Aatif Ali ◽  
Hussam Alrabaiah ◽  
Saif Ullah ◽  
Muhammad Altaf Khan ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Model Parameters ◽  
Disease Dynamics ◽  
Threshold Parameter ◽  
Fractional Model ◽  
Infected People ◽  
Fractional Models ◽  
Disease Epidemics ◽  
The Impact

AbstractCOVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained $\mathcal{R}_{0} \approx 1.50$ R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams–Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

Implications of Using Dual Number Derivatives With a Numerical Solution

2013 ◽  
Author(s):  
Suryanarayana R. Pakalapati ◽  
Hayri Sezer ◽  
Ismail B. Celik
Keyword(s):  
Automatic Differentiation ◽  
Numerical Solutions ◽  
Computer Code ◽  
Model Parameters ◽  
Model Parameter ◽  
Systematic Assessment ◽  
Dual Number ◽  
Advection Diffusion Equation ◽  
Model Equations ◽  
Derivatives Of

Dual number arithmetic is a well-known strategy for automatic differentiation of computer codes which gives exact derivatives, to the machine accuracy, of the computed quantities with respect to any of the involved variables. A common application of this concept in Computational Fluid Dynamics, or numerical modeling in general, is to assess the sensitivity of mathematical models to the model parameters. However, dual number arithmetic, in theory, finds the derivatives of the actual mathematical expressions evaluated by the computer code. Thus the sensitivity to a model parameter found by dual number automatic differentiation is essentially that of the combination of the actual mathematical equations, the numerical scheme and the grid used to solve the equations not just that of the model equations alone as implied by some studies. This aspect of the sensitivity analysis of numerical simulations using dual number auto derivation is explored in the current study. A simple one-dimensional advection diffusion equation is discretized using different schemes of finite volume method and the resulting systems of equations are solved numerically. Derivatives of the numerical solutions with respect to parameters are evaluated automatically using dual number automatic differentiation. In addition the derivatives are also estimated using finite differencing for comparison. The analytical solution was also found for the original PDE and derivatives of this solution are also computed analytically. It is shown that a mathematical model could potentially show different sensitivity to a model parameter depending on the numerical method employed to solve the equations and the grid resolution used. This distinction is important since such inter-dependence needs to be carefully addressed to avoid confusion when reporting the sensitivity of predictions to a model parameter using a computer code. A systematic assessment of numerical uncertainty in the sensitivities computed using automatic differentiation is presented.

scholarly journals Spatio-temporal modeling of surface runoff in ungauged sub-catchments of Subarnarekha river basin using SWAT

MAUSAM ◽  
2021 ◽  
Vol 72 (3) ◽  
pp. 597-606
Author(s):  
CHINMAYA PANDA ◽  
DWARIKA MOHAN DAS ◽  
B. C. SAHOO ◽  
B. PANIGRAHI ◽  
K. K. SINGH
Keyword(s):  
Surface Runoff ◽  
Assessment Tool ◽  
Nutrient Loss ◽  
Coefficient Of Determination ◽  
Annual Rainfall ◽  
Model Parameters ◽  
Runoff Generation ◽  
Temporal Modeling ◽  
Spatio Temporal ◽  
R Factors

In this present study, Soil and Water Assessment Tool (SWAT) embedded with ArcGIS interface has been used to simulate the surface runoff from the un-gauged sub-catchments in the upper catchment of Subarnarekha basin. Model calibration and validation were performed with the help of Sequential Uncertainty Fitting (SUFI-2) in-built in the SWAT-CUP package (SWAT Calibration Uncertainty Programs). The model was calibrated for a period from 1996 to 2008 with 3 years warm up period (1996-1998) and validated for a period of 5 years from 2009 to 2013. The model evaluation was performed by Nash - Sutcliffe coefficient (NSE), Coefficient of determination (R2) and Percentage Bias (PBIAS). The degree of uncertainty was evaluated by P and R factors. Basing upon the R2, NSE and PBIAS values respectively, of the order of 0.90, 0.90 and -12%, during calibration and 0.85, 0.83 and -15% during validation, substantiate performance of the model. All uncertainties of model parameters have been well taken by the P and R factors respectively, of the order of 0.95 and 0.77 during calibration and 0.82 and 0.87 during validation. The runoff generation from 19 sub-catchments of Adityapur catchment varies from 29.2-44.1% of the annual rainfall and average surface runoff simulated for the entire catchment is 545 mm. As the surface runoff generated in most of the sub-catchments amounts to above 30% of rainfall, it is recommended for adequate number of structural interventions at appropriate locations in the catchment to store the rainfall excess for providing irrigation, recharging groundwater and restricting the sediment and nutrient loss.

scholarly journals MODELLING THE RESPONSE OF VASCULAR TUMOURS TO CHEMOTHERAPY: A MULTISCALE APPROACH

2006 ◽  
Vol 16 (supp01) ◽  
pp. 1219-1241 ◽  
Author(s):  
HELEN M. BYRNE ◽  
MARKUS R. OWEN ◽  
TOMAS ALARCON ◽  
JAMES MURPHY ◽  
PHILIP K. MAINI
Keyword(s):  
Cell Density ◽  
Tumour Cell ◽  
Drug Transport ◽  
Angiogenic Factors ◽  
Future Research ◽  
Model Parameters ◽  
Multiscale Approach ◽  
Proliferating Cells ◽  
Vascular Adaptation ◽  
Spatio Temporal

An existing multiscale model is extended to study the response of a vascularised tumour to treatment with chemotherapeutic drugs which target proliferating cells. The underlying hybrid cellular automaton model couples tissue-level processes (e.g. blood flow, vascular adaptation, oxygen and drug transport) with cellular and subcellular phenomena (e.g. competition for space, progress through the cell cycle, natural cell death and drug-induced cell kill and the expression of angiogenic factors). New simulations suggest that, in the absence of therapy, vascular adaptation induced by angiogenic factors can stimulate spatio-temporal oscillations in the tumour's composition. Numerical simulations are presented and show that, depending on the choice of model parameters, when a drug which kills proliferating cells is continuously infused through the vasculature, three cases may arise: the tumour is eliminated by the drug; the tumour continues to expand into the normal tissue; or, the tumour undergoes spatio-temporal oscillations, with regions of high vascular and tumour cell density alternating with regions of low vascular and tumour cell density. The implications of these results and possible directions for future research are also discussed.

scholarly journals Prediction of peak and termination of novel coronavirus COVID-19 epidemic in Iran

2020 ◽  
Vol 31 (11) ◽  
pp. 2050152
Author(s):  
Sepehr Rafieenasab ◽  
Amir-Pouyan Zahiri ◽  
Ehsan Roohi
Keyword(s):  
Statistical Data ◽  
Sir Model ◽  
Model Parameters ◽  
Peak Time ◽  
Infected People ◽  
Epidemic Curve ◽  
Immunization Rates ◽  
Long Time ◽  
Novel Coronavirus ◽  
Official Data

The growth and development of COVID-19 transmission have significantly attracted the attention of many societies, particularly Iran, that have been struggling with this contagious, infectious disease since late February 2020. In this study, the known “Susceptible-Infectious-Recovered (SIR)” and some other mathematical approaches were used to investigate the dynamics of the COVID-19 epidemic to provide a suitable assessment of the COVID-19 virus epidemic in Iran. The epidemic curve and SIR model parameters were obtained with the use of Iran’s official data. The recovered people were considered alongside the official number of confirmed victims as the reliable long-time statistical data. The results offer important predictions of the COVID-19 virus epidemic such as the realistic number of victims, infection rate, peak time and other characteristics. Besides, the effectiveness of infection and immunization rates to the number of infected people and epidemic end time are reported. Finally, different suggestions for decreasing victims are offered.

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