The deadly Coronavirus disease (COVID-19) which was first reported in the city of Wuhan in china is one of the most deadly epidemics the world has ever experienced. From Wuhan, it rapidly spread throughout the globe, that on the 11th of March 2020, it was declared a global pandemic by the World Health Organization (WHO). It is still spreading to date and has infected over 183 million and killed over 3.9 million people the world over. Infected individuals have symptoms like high fever, fatigue, muscle pains, loss or change of taste or smell, shortness of breath, dry cough, and sore throat.
The disease can be contracted by susceptible individuals when they come in contact with respiratory droplets from infected individuals and through direct contact with contaminated surfaces. As of June 2021, there is no cure for COVID-19, affected nations only rely on protective measures such as wearing face masks in public places, social distancing, maintaining proper hygiene and ventilation, quarantine, contact tracing, and vaccination to control the disease spread.
Recently studies have revealed that individuals infected with diseases like diabetes, lung disease and heart disease, HIV/AIDS, hypertension have a compromised immune system and thus are at higher risk of contracting COVID-19 and an increased risk of severe illness upon infection. Comorbidity is defined as a disease or medical condition unrelated in etiology or causality to the principal diagnosis that coexists with the disease of interest. According to a research study in China which monitored 344 COVID-19 patients in the ICU. The majority of those that died from the disease had at least one comorbidity, about 144 of them having hypertension. Another study conducted in China showed that 247 out of 633 COVID-19 patients had at least one comorbidity. In the USA, the Centers for Disease Control and Prevention (CDC) used COVID-NET in 14 states to monitor the demographics of COVID-19 patients who were hospitalized. The results obtained from March 1 to 30, 2020, showed that, out of the 180 patients on COVID-NET, 89.3% of them had an underlying comorbidity. The most common comorbidities found were obesity, hypertension, and diabetes mellitus. These results, therefore, point towards the need to investigate the dynamics of COVID-19 and comorbidity co-infections.
Mathematical modelling has played a major role in controlling many epidemics on the globe because, in the absence of real data, models provide both qualitative and quantitative information that help in minimizing the spread of many diseases. Recently, several integer order mathematical models on COVID-19 and comorbidities have been developed to analyse the impact of various comorbidities on COVID-19 transmission. However, integer-order models have a major setback: the lack of hereditary memory effect for accurate predictions. Fractional-order derivatives on the other hand have become a powerful tool in modeling in the recent times because of their characterization. These operators possess memory effect crossover property and have statistical interpretation which makes the operators efficient. There are several different fractional-order derivatives but the most common one is the Caputo derivative which is just a power law with a local singular kernel. We also have the Caputo-Fabrizio (CF) fractional order derivative with non-singular Kernel proposed by Caputo and Fabrizio. Further properties of the CF operators were later developed by Losada and Nieto. The effectiveness of the CF operator has been illustrated in many fractional-order models.
In this work, we examined the dynamics of coronavirus with comorbidity in a community. The steady states of the model were established and reproduction number was also determined. Exponential law was applied to study the dynamics of the coronavirus with comorbidity by establishing the existence and uniqueness of solutions of the model using fixed point theory. A fractional stochastic approach in the light of exponential decay law was employed to analyse the same model. The numerical simulation results suggested that fractional-order derivative and parameter values have a serious impact on the dynamics of the fractional coronavirus with a comorbidity model. Similar results were obtained for the stochastic model, However, unlike the fractional-order model, the stochastic model exhibits some random effect. From an epidemiological viewpoint, comorbidity individuals acquire more re-infection due to lack of surveillance and precautions. It is recommended that complex phenomena be investigated using the fractional stochastic perspectives in order to present the randomness nature of the spread of many diseases.
Author: Dr. Fatmawati, M.Si
Detailed information can be seen on our article at:
http://www.scik.org/index.php/cmbn/article/view/6964
Authors: E. Bonyah, M. Juga, Fatmawati.
Title: Fractional Dynamics of Coronavirus with Comorbidity via Caputo-Fabrizio Derivative.
doi.org/10.28919/cmbn/6964
