Prediction of Cumulative Death Cases in The United States Due to COVID-19 Using Mathematical Models

Abstract


 
 
 
 In this paper, we present different growth models such as Von Bertalanffy, Baranyi-Roberts, Morgan-Mercer-Flodin (MMF), modified Richards, modified Gompertz, modified Logistics and Huang in fitting and analyzing the epidemic trend of COVID-19 in the form of total number of death cases of SARS-COV-2 in The United States as of 20th of July 2020. The MMF model was found to be the best model with the highest adjusted R2 value with the lowest RMSE value. The accuracy and bias factors values were close to unity (1.0). The parameters obtained from the MMF model include maximum growth of death rate (log) of 0.048 (95% ci from 0.047 to 0.048), curve constant (d) that affects the inflection point of 2.34 (95% ci from 2.31 to 2.38) and maximal total number of death (ymax) of 151,356 (95% ci from 147,911 to 154,525). The MMF predicted that the total number of death cases for The United States on the coming 20th of August and 20th of September 2020 will be 148,183 (95% ci of 149,199 to 147,173) and 153,780 (95% ci of 152,640 to 154,928), respectively. The predictive ability of the model utilized in this study is a powerful tool for epidemiologist to monitor and assess the severity of COVID-19 in The United States in months to come. However, as with any other model, these values need to be taken with caution due to the unpredictability of the COVID-19 situation locally and globally.
 
 
 

Runs Test for the Residuals of The Morgan-Mercer-Flodin (MMF) Model Used for Modelling the Total Number of Covid-19 Cases for Brazil

“…Organisms growth including viral infection cases over time usually exhibit a sigmoidal growth profile that exhibits lag time (λ), acceleration to a maximal value (µm) and a final phase where the rate decreases and eventually reaches zero or an asymptote (A) is observed [19]. The sigmoidal curve can be fitted by different mathematical functions, such as Logistic [19,20], modified Gompertz [19,21], Richards [19,22], Schnute [19,23], Baranyi-Roberts [24], Von Bertalanffy [19,[25][26][27], Buchanan three-phase [28,29], Huang [30][31][32][33] and Morgan-Mercer-Flodin (MMF) [34][35][36][37][38][39][40][41][42][43][43][44][45][46][47]. For the analysis of the COVID-19 pandemic [8], strong predictive ability was employed models, such as updated Gompertz and Bertalanffy and logistics.…”

“…For the analysis of the COVID-19 pandemic [8], strong predictive ability was employed models, such as updated Gompertz and Bertalanffy and logistics. The total infection case of SARS-CoV-2 in Brazil as of 15 th of July 2020 to the 20 th of December 2020 was modelled using several primary growth models with the MMF models found to be the best [41,42,44,46,[48][49][50][51].…”