ABSTRACT
We propose a theoretical study to investigate the spread of the SARS-CoV-2 virus, reported in Wuhan, China. We develop a mathematical model based on the characteristic of the disease and then use fractional calculus to fractionalize it. We use the Caputo-Fabrizio operator for this purpose. We prove that the considered model has positive and bounded solutions. We calculate the threshold quantity of the proposed model and discuss its sensitivity analysis to find the role of every epidemic parameter and the relative impact on disease transmission. The threshold quantity (reproductive number) is used to discuss the steady states of the proposed model and to find that the proposed epidemic model is stable asymptotically under some constraints. Both the global and local properties of the proposed model will be performed with the help of the mean value theorem, Barbalat’s lemma, and linearization. To support our analytical findings, we draw some numerical simulations to verify with graphical representations.
ABSTRACT
Objective: The present investigation aims on the clinical attributes and haematological parameters between symptomatic (COVID-19 ICU) and asymptomatic (COVID-19 homes isolation) patients as predisposing sign for COVID-19 related mortality. Materials and Methods: A retrospective cohort research was conducted of admitted patients to ICU, who were suffering from severe COVID-19 in Aseer Central Hospital, Abha, Kingdom of Saudi Arabia (KSA) from July 2020 until September 2020. The study included individuals with COVID -19 and ICU admission as symptomatic group and others who are COVID-19 positives with quarantine as asymptomatic group. Epidemiological, clinical and haematological laboratory data were retrospectively collected, analysed with control subjects. Results: Of the 38 ICU patients studied, the most common symptoms were fever and respiratory distress (100%), cough (86.8%). Majority were of Saudi origin (78.9%). Eighteen (47.4%) COVID-19 ICU patients showed leukocytosis, 6 (15.8%) had severe thrombocytopenia (with most having thrombocytopenia), 18 (47.4%) were anaemic. A significant correlation was observed between the WBC, RBC, Hb, platelets, neutrophil and lymphocyte count between ICU inmates compared with quarantine (p < 0.001) and RBC, Hb, neutrophil and lymphocyte count with control groups (p < 0.001). Conclusion: From the observations it is evident that, the blood tests have potential clinical value in predicting COVID-19 progression. Further, patient characteristics including age, leukocyte count, RBC, platelets and differential leukocyte counts may be significant predictors for monitoring the progression of the critical illness observed in SARS-COV-2 patients. Also, treatment procedures can be re-defined further to reduce COVID-19 mortalities in more critically ill COVID-19 individuals.
ABSTRACT
We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when R 0 < 1 at the disease-free case. For R 0 ≤ 1 , we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is R 0 ≈ 1 . 7372 . We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.