Study of SEIR epidemic model and scenario analysis of COVID-19 pandemic

Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings.

An innovative ensemble model based on multiple neural networks and a novel heuristic optimization algorithm for COVID-19 forecasting

During the global fight against the novel coronavirus pneumonia (COVID-19) epidemic, accurate outbreak trend forecasting has become vital for outbreak prevention and control. Effective COVID-19 outbreak trend prediction remains a complex and challenging issue owing to the significant fluctuations in the COVID-19 data series. Most previous studies have limitations only using individual forecasting methods for outbreak modeling, ignoring the combination of the advantages of different prediction methods, which may lead to insufficient results. Therefore, this paper develops a novel ensemble paradigm based on multiple neural networks and a novel heuristic optimization algorithm. First, a new hybrid sine cosine algorithm-whale optimization algorithm (SCWOA) is exercised on 15 benchmark tests. Second, four neural networks are used as predictors for the COVID-19 outbreak forecasting. Each predictor is given a weight, and the proposed SCWOA is used to optimize the best matching weights of the ensemble model. The daily COVID-19 series collected from three of the most-affected countries were taken as the test cases. The experimental results demonstrate that different neural network models have different performances in various complex epidemic prediction scenarios. The SCWOA-based ensemble model can outperform all comparable models with its high accuracy and robustness.

Dynamic behavior analysis of an SVIR epidemic model with two time delays associated with the COVID-19 booster vaccination time

Since the outbreak of COVID-19, there has been widespread concern in the community, especially on the recent heated debate about when to get the booster vaccination. In order to explore the optimal time for receiving booster shots, here we construct an SVIR model with two time delays based on temporary immunity. Second, we theoretically analyze the existence and stability of equilibrium and further study the dynamic properties of Hopf bifurcation. Then, the statistical analysis is conducted to obtain two groups of parameters based on the official data, and numerical simulations are carried out to verify the theoretical analysis. As a result, we find that the equilibrium is locally asymptotically stable when the booster vaccination time is within the critical value. Moreover, the results of the simulations also exhibit globally stable properties, which might be more beneficial for controlling the outbreak. Finally, we propose the optimal time of booster vaccination and predict when the outbreak can be effectively controlled.

Clinical effects of 2-DG drug restraining SARS-CoV-2 infection: A fractional order optimal control study

Fractional calculus is very convenient tool in modeling of an emergent infectious disease system comprising previous disease states, memory of disease patterns, profile of genetic variation etc. Significant complex behaviors of a disease system could be calibrated in a proficient manner through fractional order derivatives making the disease system more realistic than integer order model. In this study, a fractional order differential equation model is developed in micro level to gain perceptions regarding the effects of host immunological memory in dynamics of SARS-CoV-2 infection. Additionally, the possible optimal control of the infection with the help of an antiviral drug, viz. 2-DG, has been exemplified here. The fractional order optimal control would enable to employ the proper administration of the drug minimizing its systematic cost which will assist the health policy makers in generating better therapeutic measures against SARS-CoV-2 infection. Numerical simulations have advantages to visualize the dynamical effects of the immunological memory and optimal control inputs in the epidemic system.

Application of Gaussian process regression as a surrogate modeling method to assess the dynamics of COVID-19 propagation

In this research, we aimed to assess the possibility of using surrogate modeling methods to replace time-consuming calculations related to modeling of COVID-19 dynamics. The Gaussian process regression (GPR) was used as a surrogate to replace detailed simulations by a COVID-19 multiagent model. Experiments were conducted with various kernels, as a result, in accordance with the quality metrics of the models, kernels were identified in which the surrogate gives the most accurate result (Rational Quadratic kernel and Additive kernel). It was demonstrated that by smoothing the dynamics of COVID-19 propagation, it is possible to achieve greater accuracy in GPR training. The obtained results prove the potential possibility of using surrogate modeling methods to conduct an uncertainty quantification of the multiagent model of COVID-19 propagation.

Trade-Off between COVID-19 Pandemic Prevention and Control and Economic Stimulus

The coronavirus disease 2019 (COVID-19) pandemic has posed a severe threat to public health and economic activity. Governments all around the world have taken positive measures to, on the one hand, contain the epidemic spread and, on the other hand, stimulate the economy. Without question, tightened anti-epidemic policy measures restrain people's mobility and deteriorate the levels of social and economic activity. Meanwhile, loose policy measures bring little harm to the economy temporarily but could accelerate the transmission of the virus and ultimately wreck social and economic development. Therefore, these two kinds of governmental decision-making behaviors usually conflict with each other. With the purpose of realizing optimal socio-economic benefit over the full duration of the epidemic and to provide a helpful suggestion for the government, a trade-off is explored in this paper between the prevention and control of the epidemic, and economic stimulus. First, the susceptible-infectious-recovered (SIR) model is introduced to simulate the epidemic dynamics. Second, a state equation is constructed to describe the system state variable-the level of socio-economic activity dominated by two control variables. Specifically, these two variables are the strengths of the measures taken for pandemic prevention and control, and economic stimulus. Then, the objective function used to maximize the total socio-economic benefit over the epidemic's duration is defined, and an optimal control problem is developed. The statistical data of the COVID-19 epidemic in Wuhan are used to validate the SIR model, and a COVID-19 epidemic scenario is used to evaluate the proposed method. The solution is discussed in both static and dynamic strategies, according to the knowledge of the epidemic's duration. In the static strategy, two scenarios with different strengths (in terms of anti-epidemic and economic stimulus measures) are analyzed and compared. In the dynamic strategy, two global optimization algorithms, including the dynamic programming (DP) and Pontryagin's minimum principle (PMP), respectively, are used to acquire the solutions. Moreover, a sensitivity analysis of model parameters is conducted. The results demonstrate that the static strategy, which is independent of the epidemic's duration and can be easily solved, is capable of finding the optimal strengths of both policy measures. Meanwhile, the dynamic strategy, which generates global optimal trajectories of the control variables, can provide the path that leads to attaining the optimal total socio-economic benefit. The results reveal that the optimal total socio-economic benefit of the dynamic strategy is slightly higher than that of the static strategy.

A (2+1)-Dimensional Fractional-Order Epidemic Model with Pulse Jumps for Omicron COVID-19 Transmission and Its Numerical Simulation

In this paper, we would like to propose a (2+1)-dimensional fractional-order epidemic model with pulse jumps to describe the spread of the Omicron variant of COVID-19. The problem of identifying the involved parameters in the proposed model is reduced to a minimization problem of a quadratic objective function, based on the reported data. Moreover, we perform numerical simulation to study the effect of the parameters in diverse fractional-order cases. The number of undiscovered cases can be calculated precisely to assess the severity of the outbreak. The results by numerical simulation show that the degree of accuracy is higher than the classical epidemic models. The regular testing protocol is very important to find the undiscovered cases in the beginning of the outbreak.