Nonlinear dynamics modeling and epidemic forecast of COVID-19

To study the spreading trend and risk of COVID-19, according to the characteristics of COVID-19, this paper proposes a new transmission dynamic model named SLIR(susceptible-low-risk-infected-recovered), based on the classic SIR model by considering government control and personal protection measures. The equilibria, stability and bifurcation of the model are analyzed to reveal the propagation mechanism of COVID-19. In order to improve the prediction accuracy of the model, the least square method is employed to estimate the model parameters based on the real data of COVID-19 in the United States. Finally, the model is used to predict and analyze COVID-19 in the United States. The simulation results show that compared with the traditional SIR model, this model can better predict the spreading trend of COVID-19 in the United States, and the actual official data has further verified its effectiveness. The proposed model can effectively simulate the spreading of COVID-19 and help governments choose appropriate prevention and control measures. Copyright ©2023 Control and Decision.

Dynamics Modeling and Analysis of COVID-19

To study the spreading mechanism and risk and predict the spreading trend of COVID-19, and provide supports for the government to formulate prevention and control policies, a new nonlinear dynamic model, i.e., the susceptible-low risk-exposed-infectious-removed (SLEIR) model is proposed, and the population with protection measures is regarded as a low-risk group and included into this model. The basic reproduction number, equilibrium, stability and bifurcation are analyzed to reveal the spreading mechanism, and the data on COVID-19 in India is used for least-squares fitting of model parameters and some initial values. The fitted parameters are used to predict the spreading trend in India. Predicting results show that the average relative errors of the epidemic prediction are 4.107% and 2.805% from March to April and from April to May, respectively. For the latest epidemic prediction of India in October, the average relative error is 3.266%. These simulations indicate that the proposed model can accurately predict COVID-19 spreading in India, is more suitable for analyzing its spreading in India with higher prediction accuracy compared with the traditional SEIR model, and can provide technical support for the government of India to select prevention and control measures. © 2022, Editorial Office of Journal of Xi'an Jiaotong University. All right reserved.

Time Series Analysis of Infected COVID-19 Cases in the Zamboanga Peninsula, Philippines using Long Short-Term Memory Neural Networks

Infectious disease outbreaks, such as COVID-19 pandemics, exhibit patterns that can be described by the dynamics of a mathematical model This study seeks to explore the use of LSTM in order to develop models that will capture the non-linear dynamic changes of COVID-19 cases in Zamboanga Peninsula. The study uses 436 data points where the latest timestamp for the dataset is on May 29, 2021 and the oldest is on March 20, 2020. These data are taken from the DOH repositories and revalidated using the data from the DOH Regional Office. The training and testing phase results show that among the different LSTM variants, convLSTM trained using Adam and RMSProp attained the smallest RMSE result of 42.34 and 43.67 and a correlation coefficient of 0.94 0.93, respectively. ConvLSTM, when trained with Adam and RMSProp, produces the best results, as evidenced by the shortest RMSE and highest correlation coefficient. Results revealed that convLSTM appears to be a viable choice for modeling the time series of the COVID 19 infected cases in Zamboanga Peninsula Region in compared with the different variants of LSTM. © 2021 IEEE.

Linear and non-linear dynamics of the epidemics: System identification based parametric prediction models for the pandemic outbreaks.

Coronavirus disease 2019 (COVID-19) has endured constituting formidable economic, social, educational, and phycological challenges for the societies. Moreover, during pandemic outbreaks, the hospitals are overwhelmed with patients requiring more intensive care units and intubation equipment. Therein, to cope with these urgent healthcare demands, the state authorities seek ways to develop policies based on the estimated future casualties. These policies are mainly non-pharmacological policies including the restrictions, curfews, closures, and lockdowns. In this paper, we construct three model structures of the SpInItIbD-N (suspicious Sp, infected In, intensive care It, intubated Ib, and dead D together with the non-pharmacological policies N) holding two key targets. The first one is to predict the future COVID-19 casualties including the intensive care and intubated ones, which directly determine the need for urgent healthcare facilities, and the second one is to analyse the linear and non-linear dynamics of the COVID-19 pandemic under the non-pharmacological policies. In this respect, we have modified the non-pharmacological policies and incorporated them within the models whose parameters are learned from the available data. The trained models with the data released by the Turkish Health Ministry confirmed that the linear SpInItIbD-N model yields more accurate results under the imposed non-pharmacological policies. It is important to note that the non-pharmacological policies have a damping effect on the pandemic casualties and this can dominate the non-linear dynamics. Herein, a model without pharmacological or non-pharmacological policies might have more dominant non-linear dynamics. In addition, the paper considers two machine learning approaches to optimize the unknown parameters of the constructed models. The results show that the recursive neural network has superior performance for learning nonlinear dynamics. However, the batch least squares outperforms in the presence of linear dynamics and stochastic data. The estimated future pandemic casualties with the linear SpInItIbD-N model confirm that the suspicious, infected, and dead casualties converge to zero from 200000, 1400, 200 casualties, respectively. The convergences occur in 120 days under the current conditions.

A model for social spreading of Covid-19: Cases of Mexico, Finland and Iceland.

The shocking severity of the Covid-19 pandemic has woken up an unprecedented interest and accelerated effort of the scientific community to model and forecast epidemic spreading to find ways to control it regionally and between regions. Here we present a model that in addition to describing the dynamics of epidemic spreading with the traditional compartmental approach takes into account the social behaviour of the population distributed over a geographical region. The region to be modelled is defined as a two-dimensional grid of cells, in which each cell is weighted with the population density. In each cell a compartmental SEIRS system of delay difference equations is used to simulate the local dynamics of the disease. The infections between cells are modelled by a network of connections, which could be terrestrial, between neighbouring cells, or long range, between cities by air, road or train traffic. In addition, since people make trips without apparent reason, noise is considered to account for them to carry contagion between two randomly chosen distant cells. Hence, there is a clear separation of the parameters related to the biological characteristics of the disease from the ones that represent the spatial spread of infections due to social behaviour. We demonstrate that these parameters provide sufficient information to trace the evolution of the pandemic in different situations. In order to show the predictive power of this kind of approach we have chosen three, in a number of ways different countries, Mexico, Finland and Iceland, in which the pandemics have followed different dynamic paths. Furthermore we find that our model seems quite capable of reproducing the path of the pandemic for months with few initial data. Unlike similar models, our model shows the emergence of multiple waves in the case when the disease becomes endemic.

Forecasting the 2020 COVID-19 Epidemic: A Multivariate Quasi-Poisson Regression to Model the Evolution of New Cases in Chile.

Objectives: To understand and forecast the evolution of COVID-19 (Coronavirus disease 2019) in Chile, and analyze alternative simulated scenarios to better predict alternative paths, in order to implement policy solutions to stop the spread and minimize damage. Methods: We have specified a novel multi-parameter generalized logistic growth model, which does not only look at the trend of the data, but also includes explanatory covariates, using a quasi-Poisson regression specification to account for overdispersion of the count data. We fitted our model to data from the onset of the disease (February 28) until September 15. Estimating the parameters from our model, we predicted the growth of the epidemic for the evolution of the disease until the end of October 2020. We also evaluated via simulations different fictional scenarios for the outcome of alternative policies (those analyses are included in the Supplementary Material). Results and Conclusions: The evolution of the disease has not followed an exponential growth, but rather, stabilized and moved downward after July 2020, starting to increase again after the implementation of the Step-by-Step policy. The lockdown policy implemented in the majority of the country has proven effective in stopping the spread, and the lockdown-relaxation policies, however gradual, appear to have caused an upward break in the trend.