Mathematical modelling performs a vital part in estimating and controlling the recent outbreak of coronavirus disease 2019 (COVID-19). In this epidemic, most countries impose severe intervention measures to contain the spread of COVID-19. The policymakers are forced to make difficult decisions to leverage health and economic development. How and when to make clinical and public health decisions in an epidemic situation is a challenging question. The most appropriate solution is based on scientific evidence, which is mainly dependent on data and models. So one of the most critical problems during this crisis is whether we can develop reliable epidemiological models to forecast the evolution of the virus and estimate the effectiveness of various intervention measures and their impacts on the economy. There are numerous types of a mathematical model for epidemiological diseases.
The coronavirus disease 2019 (COVID-19), declared as a pandemic by the World Health Organization at the end of January 2020, is considered to be the most devastating infectious disease outbreak ever since the 1918 influenza pandemic. The first case of COVID-19 was reported on 31 December 2019 in Wuhan China, which was initially identified as the epicentre of the virus.1 Given it is apparently able to generate rapid and substantial human-to-human transmissions, COVID-19 has largely been spreading in vast geographic regions including more than 200 countries and severely hit countries such as Iran, Italy, Spain, France, Germany, UK, and the US, etc. As of 19 April 2020, about 2 394 278 confirmed cases including more than 164 937 deaths had been reported worldwide according to the COVID-19 map by the Johns Hopkins University,2 which reveals that the epicentre is gradually moving to Europe and America.
In general, an epidemic follows a similar tendency, which can be modelled mathematically. Initially, the number of infected cases progressively increased, which usually exhibits exponential behaviour. On reaching the peak, it then turns over and gradually decreases. Ultimately, the outbreak fades out to zero, which implies the end of the epidemic. From the data in Ref. 4. we can observe from Fig. 1a that the infected cases in China started to grow in January 2020 and there was a sudden increase within a single day in February 2020 due to the change of diagnostic methods. Then the curve of China began to be saturated after early March.
Mathematical models are efficient tools to understand the ongoing trends for COVID-19. The models are essential to make a therapeutic choice when surge capacity has been exceeded or without ready access to laboratory testing.8 The models are crucial for the policymaker to acquire medical supplies, allocate human resources and hospital beds, and ensure the sustainability of the health system throughout the peak and duration of the epidemic.8 Researchers around the world have performed numerous mathematical modelling and numerical analysis on COVID-19
since its outbreak. In the following section, we review these proposed methods and present the updated results with a focus on the following topics: fatality ratio, disease tendency, basic reproduction numbers, asymptomatic infective, herd immunity, and the effects of intervention measures.
Severity is one of the most concerning factors in the outbreak of a pandemic. The fatality ratio is a crucial measurement to describe the severity of the transmittable disease. It is a challenging task to predict the fatality rate as it changes over time and can be measured in many different ways during an epidemic. The case fatality ratio (CFR) is a standard measurement that estimates the proportion of deaths from the disease to the total number of cases diagnosed with the disease.
