Abstract
The SIR type models are built by a set of ordinary differential equations (ODE), which are strongly initial value dependant. To fit multiple biological data with SIR type equations requires fitting coefficients of these equations by an initial guess and applying optimization methods. These coefficients are also extremely initial value-dependent. In the vast publication of these types, we hardly see, among simple to highly complicated SIR type methods, that these methods presented more than a maximum of two biological data sets. We propose a novel method that integrates an analytical solution of the infectious population using Weibull distribution function into any SIR type models. The Weibull-SIRD method has easily fitted 4 set of COVID-19 biological data simultaneously. It is demonstrated that the Weibull-SIRD method predictions for susceptible, infected, recovered, and deceased populations from COVID-19 in Kuwait and UAE are superior compared with SIRD original ODE model. The proposed method here opens doors for new deeper studying of biological dynamic systems with realistic biological data trends than providing some complicated, cumbersome mathematical methods with little insight into biological data's real physics.
Highlights
Since the outbreak of the novel coronavirus (COVID-19) in Wuhan, China in December 2019, the world has experienced the worst pandemic in history; not in terms of fatality but in the way we have used to live and commute around world
The SIR type models are built by a set of ordinary differential equations (ODE), which are strongly initial value dependant
We propose a novel method that integrates an analytical solution of the infectious population using Weibull distribution function into any SIR type models
Summary
Since the outbreak of the novel coronavirus (COVID-19) in Wuhan, China in December 2019, the world has experienced the worst pandemic in history; not in terms of fatality but in the way we have used to live and commute around world. Exact solutions of SIR model were reported in a number of publications; these solutions hardly fit with actual data from a pandemic. Bohner et al [2] provided a nice article on Bailey’s [3] SIR model's exact solution In such methods, the recovered (R) population is ignored when solving susceptible (S) and infectious (I) equations; we couldn’t fit the COVID-data with the explicit formulations provided. Shabbir et al [5] and Maliki [6] have both reported exact solutions to SIS and SIR original ODE equations reported by Kermack and McKendrick [7] These special models included (S) and (I) equations only. The present formulation provides fast and robust solutions to SIRD equations and can be used to optimize the highest prediction of an epidemic/pandemic. Results of COVID-19 dynamics are discussed for Kuwait and UAE, and the prediction capability of the new model is presented, and conclusions are drawn
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