Modeling and multi-objective optimal control of reaction-diffusion COVID-19 system due to vaccination and patient isolation.

In this paper, a reaction-diffusion COVID-19 model is proposed to explore how vaccination-isolation strategies affect the development of the epidemic. First, the basic dynamical properties of the system are explored. Then, the system's asymptotic distributions of endemic equilibrium under different conditions are studied. Further, the global sensitivity analysis of R 0 is implemented with the aim of determining the sensitivity for these parameters. In addition, the optimal vaccination-isolation strategy based on the optimal path is proposed. Meantime, social cost C ( m , σ ) , social benefit B ( m , σ ) , threshold R 0 ( m , σ ) three objective optimization problem based on vaccination-isolation strategy is explored, and the maximum social cost ( M S C ) and maximum social benefit ( M S B ) are obtained. Finally, the instance prediction of the Lhasa epidemic in China on August 7, 2022, is made by using the piecewise infection rates ß 1 ( t ) , ß 2 ( t ) , and some key indicators are obtained as follows: (1) The basic reproduction numbers of each stage in Lhasa, China are R 0 ( 1 : 8 ) = 0.4678 , R 0 ( 9 : 20 ) = 2.7655 , R 0 ( 21 : 30 ) = 0.3810 and R 0 ( 31 : 100 ) = 0.7819 ; (2) The daily new cases of this epidemic will peak at 43 on the 20th day (August 26, 2022); (3) The cumulative cases in Lhasa, China will reach about 640 and be cleared about the 80th day (October 28, 2022). Our research will contribute to winning the war on epidemic prevention and control.

Dynamics and strategies evaluations of a novel reaction-diffusion COVID-19 model with direct and aerosol transmission.

The COVID-19 epidemic has infected millions of people and cast a shadow over the global economic recovery. To explore the epidemic's transmission law and provide theoretical guidance for epidemic prevention and control. In this paper, we investigate a novel SEIR-A reaction-diffusion COVID-19 system with direct and aerosol transmission. First, the solution's positivity and boundedness for the system are discussed. Then, the system's the basic reproduction number is defined. Further, the uniform persistence of disease when R 0 > 1 is explored. In addition, the system equilibrium's global stability based on R 0 is demonstrated. Next, the system's NSFD scheme is investigated and the discrete system's positivity, boundedness, and global properties are studied. Meantime, global sensitivity analysis on threshold R 0 is investigated. Interestingly, the effects of three strategies, including vaccination, receiving treatment, and wearing a mask, are evaluated numerically. The results suggest that the above three strategies can effectively control the peak and final scale of infection and shorten the duration of the epidemic. Finally, theoretical simulations and instance predictions are used to give several key indicators of the epidemic, including threshold R 0 , peak, time to peak, time to clear cases, and final size. The instance prediction results are as follows: (1) The basic reproduction numbers of Yangzhou and Putian in China are R 0 = 2.5107 and R 0 = 1.8846 , respectively. (2) This epidemic round in Yangzhou will peak at 56 new daily confirmed cases on the 9th day (August 5), and Putian will peat at 37 new daily confirmed cases on the 6th day (September 15). (3) The final scale of infections in Yangzhou and Putian reached 570 and 205 cases, respectively. (4) The Yangzhou epidemic is expected to be completely cleared on the 25th day (August 21). In addition, the Putian epidemic will continue for 15 days and be cleared on September 24. The analysis results mean that we should improve our immunity by actively vaccinating, reducing the possibility of aerosol transmission by wearing masks. In particular, people should maintain proper social distance, and the government should strengthen medical investment and COVID-19 project research.

Ergodic stationary distribution and extinction of a hybrid stochastic SEQIHR epidemic model with media coverage, quarantine strategies and pre-existing immunity under discrete Markov switching

Combining a deterministic SEQIHRS model proposed by Sahu et al. (2015) and the present mathematical modelling of media coverage effect (2020), a hybrid stochastic SEQIHR model, perturbed by both nonlinear white noise and colored noise, is formulated and studied for the transmission dynamics of an infectious disease with media coverage, quarantine strategies and pre-existing immunity in a community. First, we prove that the stochastic model possesses a unique global positive solution. Second, by means of the basic reproduction number R0 of the corresponding deterministic model, two relevant critical values which include R¯0 and R0C are derived. Next, we obtain the disease extinction under R0<1 and R¯0<1. Moreover, we further establish the sufficient condition R0C>1 for the existence and uniqueness of an ergodic stationary distribution of the stochastic model, which means the infectious disease will be prevailing and persistent in a community. Finally, several numerical simulations are performed to validate the above theoretical results. Besides, the impact of media coverage and nonlinear hybrid noises on the dynamical behavior of the stochastic model are studied at the end of this paper.