Abstract
The Corona (COVID-19) epidemic has triggered interest in many fields of technology, medicine, science, and politics. Most of the mathematical research in this area focused on analyzing the dynamics of the spread of the virus. In this article, after a review of some current methodologies, a non-linear system of differential equations is developed to model the spread of COVID-19. In order to consider a wide spectrum of scenarios, we propose a susceptible-exposed-infected-quarantined-recovered (SEIQRS)-model which was analyzed to determine threshold conditions for its stability, and the number of infected cases that is an infected person will transmit on a virus to, reproduction number R0 is calculated. It is established that the disease-free state is globally asymptotically stable when the reproduction number is less than unity and unstable if its value is more than one. The model is tested against real data taken from the Ministry of Health in Jordan covering three time periods between March and September 2020 wherein two infection peaks occurred in the country. Simulations show consistency and accurate spread predictions within the optimistic range and the proposed model is distinguished by its applicability to aspects including recurrent infections, asymptomatic carriers over several timespans as well as the aforementioned waves of infection.
Highlights
Introduction and Background The spread ofCOVID-19 zoonotic corona virus from December 2019, which occurred by crossing species from animals to humans similar to another two previous outbreaks, namely: i) SARS-CoV which originated in China in 2002 and left over 750 fatalities from 8000 infections that rapidly spread to 30 countries. ii) MERS-CoV was occurred in 2012 in the Kingdom of Saudi Arabia; it infected over 2500 people and left 850 fatalities [1,2]; both viruses were initially identified by in-vitro cell culture [3]
In order to consider a wide spectrum of scenarios, we propose a susceptible-exposedinfected-quarantined-recovered (SEIQRS)-model which was analyzed to determine threshold conditions for its stability, and the number of infected cases that is an infected person will transmit on a virus to, reproduction number R0 is calculated
The model is tested against real data taken from the Ministry of Health in Jordan covering three time periods between March and September 2020 wherein two infection peaks occurred in the country
Summary
The Center for Disease Control [11] define epidemiology as “the study (scientific, systematic, and datadriven) study of the distribution (frequency, pattern) and determinants (causes, risk factors) of health-related states and events (not just diseases) in specified populations (neighborhood, school, city, state, country, global).” According to [12,13], the spread of SARS-CoV-2 ignited interest in modern epidemiology, focusing on the dynamics of case detection as well as exponential spread and growth of infected cases, not to mention the associated non-medical challenges such as effective communications. The authors conclude that the SARS-CoV-2 pandemic was hitherto unique, it still offered insights seen before in other pathogens in the period between first diagnosis and vaccine development. These include: i) the disease is likely to remain a factor for a long time, and ii) the high rates of infection will force nations to choose between widespread infections or social and economic disruption. Mathematical models allow us to utilize mathematical notation to represent the behavior of a system in a precise way such that we can study and analyze the epidemic dynamics of diseases as well as the likely effects of preventative measures and vaccinations. Model weaknesses stem from: i) unknown disease attributes, ii) unknowable disease attributes or, iii) missed behavior/information that was inadvertently dropped from the model design, e.g., not picked upon early enough or was not reported
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