1 Department of Mathematics, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia

2 Graduate School of Mathematics and Applied Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia


BACKGROUND AND OBJECTIVES: The spread of COVID-19 is very fast because it is transmitted from human to human. Non-pharmaceutical control is one of the important actions in reducing the spread of COVID-19, such as the use of masks and physical distancing. This study aims to model COVID-19 by incorporating people''s habits as a non-pharmaceutical preventive measure. The model formed emphasizes the importance of preventing with masks and physical distancing. The implication of this action is that the infected population is decreasing, resulting in less interaction between the susceptible and the infected. In this case, the virus has not vanished from the community, but the use of masks in certain populations or subpopulations is lower than before, which can reduce mask waste in the environment.
METHODS: This study expands on a previous MERS-CoV research model using the susceptible-exposed-infected-quarantine-recovery model by incorporating behavioral control, specifically the use of masks and physical distancing as preventive measures. The susceptible population that interacts with the carrier/exposed and infected population is used to calculate mask use. The susceptible population was divided into two subpopulations based on their willingness to wear masks. The following breakthrough is the application of the same system to the infected population, which is required to wear masks at all times during their self-isolation period. The model-generated equation system is a nonlinear system of differential equations. The developed model is examined by determining the equilibrium point and the basic reproduction number.
FINDINGS: The model resulted an asymptotically stable disease-free equilibrium and endemic equilibrium. The disease-free stability is only examined if the compliance with physical distancing exceeds 0.55 and the compliance with the use of distancing exceeds 0.55. This compliance condition resulted in a decrease in basic reproduction number ranging from 0.48 to 0.07. The endemic stability is only investigated if compliance with physical distancing is 0.1 and compliance with use of distancing is 0.2. The endemic condition can arise if masks and physical separation are not used. Physical distancing compliance and mask use have values less than 0.1 and 0.2, respectively.
CONCLUSION: The analysis of the equilibrium points and basic reproduction numbers, show that increasing compliance in carrying out the health protocol measures of physical distancing and mask use causes a decrease in the spread of COVID-19, so that the disease will disappear over time. 

Graphical Abstract

Community behavior for mathematical model of coronavirus disease 2019 (COVID-19)


  • The disease-free equilibrium point will only occur and be stable if people adhere to masks and social distancing.
  • On the other hand, if there is no compliance with health protocols, then the endemic equilibrium point will occur and be stable.
  • Physical distancing and mask use causes a decrease in the spread of COVID-19 indicated by its reproduction number;
  • The formula is optimistic that 88% using masks and 90% physical distancing in communities can eliminate the spread of COVID-19.


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