In recent history, COVID19 is one of the worst infectious disease outbreaks currently affecting humanity globally. Using real data on the COVID19 outbreak from 22 January 2020 to 30 March 2020, we developed a mathematical model to investigate the impact of control measures in reducing the spread of the disease. Analyses of the model were carried out to determine the dynamics. The results of the analyses reveal that, using the data from China, implementing all possible control measures best reduced the rate of secondary infections. However, quarantine (isolation) of infectious individuals is shown to have the most dominant effect. This possibility emphasizes the need for extensive testing due to the possible prevalence of asymptomatic COVID19 cases.
On 31 December 2019, the World Health Organization (WHO) China Country Office received information of a case of pneumonia detected in Wuhan City, Hubei Province of China (
Globally, COVID19 resulted in exponential growth in cases and deaths from 22 January 2020 to 30 March 2020 and continued to spread rapidly. Therefore, urgent measures are needed to save humanity from this deadly outbreak.
Mathematical models have been successfully used in studying the dynamics of infectious disease outbreaks (
Some of the recommended control measures to reduce the spread of COVID19 include: sensitization of the public on how to reduce transmission, isolation/quarantine of infectious individuals, prompt treatment of infectious individuals etc. Here, we formulate a mathematical model that takes these control measures into consideration. From the mode of transmission there is some distance at which the virus cannot be transmitted. Consider a location (country, community, etc.) and let
Several control measures are introduced. Sensitization on methods that reduce an individuals chance of being infected (regular hand washing etc.) is assumed to reduce the number of susceptible individuals at a rate
The meaning of variables and parameters are given in
Variables  Meaning 

Susceptible individuals at time ( 

Exposed individuals at time ( 

Infectious individuals at time ( 

quarantine/Isolated individuals at time ( 

Recovered/Removed/Death individuals at time ( 

Individuals in the location whose probability of becoming infected is greater than zero  
Pathogens in the environment 
Parameters  Meaning 

Λ  Recruitment rate into 
Contact rate with 

Contact rate with 

Natural death rate of humans  
COVID19 induced death rate  
Rate of quarantine of 

Pathogens decay rate  
Shedding rate of pathogens  
Rate at which 

Rate of recovery for 

Rate of reduction of 

ε  Rate of reduction in contact rate of 
Since humans and pathogens have different space and time scales, it was necessary to nondimensionalized model
The model is used to investigate the dynamics of a COVID19 outbreak. First, the basic reproduction number, denoted by
The basic reproduction number (
Second, the model is fit to the real data (active cases of COVID19
Using the parameter values, the basic reproduction number for the COVID19 outbreak in China as at 30 March 2020 is
Numerical simulations enable us to explore the impact of each of the control measures used in the COVID19 outbreak in China.
Next we explore the impact of each of the various control measures.
The effect of implementing any two of the controls is presented in
COVID19 is one of the worst infectious outbreaks currently affecting humanity globally. The disease started in China around December 2019 and has spread to almost every country of the world within a very short period. The emotional and economic impact of this outbreak could be significant. Hence the necessity to urgently stop this outbreak.
Several control measures have been recommended by the World Health Organization and other policy makers. Considering existing data on the COVID19 outbreak in China has demonstrated that it is possible to reduce the spread of this disease and how they went about this control can be useful for other countries currently facing COVID 19 outbreaks. In this study, data from China was used to develop a mathematical model for a COVID19 outbreak that includes the primary control measures used.
First, epidemiological features of the model were examined using the basic reproduction number. The control parameters of the model were estimated by fitting the model to the COVID19 outbreak data from China (from 22 January 2020 to 30 March 2020). Using these fitted parameter values, the basic reproduction number for the COVID19 outbreak in China as at 30 March 2020 was
Second, by varying control parameters, numerical simulations are used to investigate levels of impact of the various control measures in reducing the spread of a COVID19 outbreak. For instance, if all control measures are effectively used the spread of the disease reduces considerably in the population. On the other hand, if no control measures are considered, our result showed that a lot more of the population can be infectious within a short period. As is well understood, in this scenario the resulting curve will result in numerous deaths and extreme pressure on health care systems. To avoid these negative effects the aim is to flatten the curve as shown for the complete control scenario.
Next, each control was applied separately to measure their effect. In each case, the level of control was prescribed by the data fitting. Only quarantining of infectious individuals has the necessary effect of flattening the curve. Thus, while the other controls are helpful and the combined controls provide the best overall control, our study suggests that isolation of infectious individuals is by far the most important control method. This result agrees with the situation in South Korea where extensive testing allowed control of new infections and largely contained the outbreak (
The results here suggest that hygiene behaviour is the least effective strategy. Although increasing each of the controls could increase their effect. Therefore, efforts are still required to educate individuals on disease prevention strategies. Forcing much of the public to keep separate by a strict lock down policy can also increase levels of control. For less developed countries, where isolation of infectious individual is difficult to apply effectively, the results here suggest that eventually lock down and personal prevention strategies applied together could lead to the end of an outbreak. However, this process would take longer adding to the associated financial burdens on individuals and the state.
All models depend on their simplifying assumptions. For example, the importance of population network structure could be important in how a disease spreads with this knowledge enabling the potential for targeted vaccine control (
A study of the public health interventions of the COVID19 outbreak in Wuhan, China found that over time multifaceted interventions improved control of the outbreak (
In China they managed to stem the spread of their COVID19 outbreak. Using the Chinese data and assumptions on how the outbreak was controlled we show using an ordinary differential equations model the possible effects of different controls. Sensitization and lockdown are helpful in controlling the disease but those would need to be strongly enforced. It seems unlikely that efforts to increase these individual controls could be significantly improved beyond the efforts in China. Thus, this study points strongly to the importance of implementing all available controls. Also, the isolation of infectious individual is possibly of particular importance which would point to the need for extensive testing due to the possible prevalence of asymptomatic COVID19 cases.
Code to calculate parameters for the COVID19 model to fit the active cases data for the COVID19 epidemic in China. This code uses the fmincon routine in the commercial software Matlab.
Code to simulate the COVID19 model runs for different scenarios. This code uses the ode45 differential equation solving routine provided in the commercial software Matlab.
We acknowledge and regret the pain and suffering that this virus has caused.
The authors declare there are no competing interests.
The following information was supplied regarding data availability:
The raw data came from the Worldometers site; both the raw data and Matlab code are available in the