The Research of SEIJR Model With Time-Delay Based on 2019-nCov

Abstract

A global epidemic disease known as the novel coronavirus (2019-nCov) had seriously hit the most area around the whole world causing unpredictable loss of manpower and finance during the past year. Modeling the spread and development of infectious diseases represented by new Coronavirus has become an important part of public health work in the world. Estimation of possible infection population and prospective suggestion of handling spread based on existing data is crucial. In this article, we build a more applicable model called SEIJR with a log-normal distributed time delay to forecast the trend of spreading considering the biology parameters obtained based on Chinese clinical data in Wuhan and the real spread feature of 2019-nCov in Italy. Adopting Particle Swarm Optimization (PSO), we estimate the early period average spreading velocity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\alpha _{0}}$ </tex-math></inline-formula> ) and implement inversion analysis of time point ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {T_{0}}$ </tex-math></inline-formula> ) when the virus first hit Italy. Based on fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\alpha _{0}}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {T_{0}}$ </tex-math></inline-formula> , we then obtained the average spreading velocity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\alpha _{1}}$ </tex-math></inline-formula> after the area lockdown using PSO. The result shows that it will help address the infection by generating the prediction trends of different <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\alpha }$ </tex-math></inline-formula> which we considered. Finally, our research applies Logistic regression, Neural Network embedding LSTM layer, which is two representative machine learning algorithms, to directly predict future infection trends and compare the forecast with results yielded by mathematical model adopting differential equations. Not only solved the complex, nondifferentiable equation of the epidemic model, this research also performs well in inversion analysis based on PSO which conveys informative outcomes for further discussion on precautious action. The comparison with the machine learning algorithms shows that the 2019-nCov based epidemic dynamics assumption is reasonable and helpful to the mathematical model, which is better than the data-driven machine learning algorithms. Code can be freely downloaded from <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/Summerwork/2019-nCov-Prediction</uri> .