# A SIR-UC EPIDEMIC MODEL: THE ANALYSIS OF SUSCEPTIBLE-INFECTED-REMOVED (SIR) EPIDEMIC MODEL WITH THE COVERAGE OF HEALTH INSURANCE (UNCOVERED AND COVERED INDIVIDUALS)

• Sutanto Sutanto Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0002-8072-1216
• Dewi Retno Sari Saputro Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0002-6569-394X
• Alexander Yonathan Christy Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Sebelas Maret, Indonesia https://orcid.org/0000-0002-9996-4891
• Aslina Baharum Department of Information System, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Malaysia https://orcid.org/0000-0003-3910-5646
Keywords: SIR Model, Epidemic Model, Insurance

### Abstract

Susceptible-Infected-Removed (SIR) model is a widely used epidemic model that simulates the spread of infectious diseases within a population. It classifies individuals into susceptible, infected, and removed states, with the number of individuals in each state being time-dependent variables denoted by S(t), I(t), and R(t), respectively. The model considers direct contact transmission between infected and susceptible individuals. In developed countries, some people cannot afford medical treatment. In contrary, the recovery rate of infected individual in the population is directly proportional to the number of people receiving medical treatment. Affordable health insurance increases the number of people receiving medical treatment thus insurance should be considered aspect in epidemic model.  The main purpose of this research is to analyze the effect of insurance on the SIR epidemic model. This research classifies individuals in both S(t) and I(t) based on their insurance coverage status. This model assumes permanent immunity for R(t), thus it is unnecessary to classify individuals in this state based on their insurance coverage status because they do not spread the disease nor have potential to be re-infected. Numerical simulation is organized to find the effect of insurance in SIR model by analyzing the equilibrium point. The result based on the equilibrium point suggests that the insurance in SIR epidemic model: (1) decrease the I(t) because it accelerate the recovery rate; (2) decrease theR(t) because there is less infected people for recovery; (3) increase the S(t) because there is less infected people to transmit the disease, compared to the SIR model without the insurance.

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Published
2024-03-01
How to Cite
[1]
S. Sutanto, D. Saputro, A. Christy, and A. Baharum, “A SIR-UC EPIDEMIC MODEL: THE ANALYSIS OF SUSCEPTIBLE-INFECTED-REMOVED (SIR) EPIDEMIC MODEL WITH THE COVERAGE OF HEALTH INSURANCE (UNCOVERED AND COVERED INDIVIDUALS)”, BAREKENG: J. Math. & App., vol. 18, no. 1, pp. 0171-0178, Mar. 2024.
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Articles