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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Sila Rizqina
Jurusan Matematika FMIPA Universitas Lambung Mangkurat
Decision Sciences, Operations Research & Management Transportation

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INVESTIGATION OF THE IMPACT OF ONE-WAY MOBILITY IN A MATHEMATICAL MODEL OF COVID-19 TRANSMISSION: STABILITY ANALYSIS AND NUMERICAL SIMULATIONS Muhammad Afief Balya; Yuni Yulida; Sila Rizqina; Hermei Lissa
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 20, No 1 (2026)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v20i1.18506

Abstract

This study develops a COVID-19 transmission model incorporating one-way human mobility between two interconnected cities to examine the epidemiological consequences of asymmetric population movement. Unlike most existing models that assume symmetric two-way mobility, and extending the no-mobility framework of (Balya et al., 2025), the proposed model introduces unidirectional population flow by allowing individuals from only one city to engage in high-mobility activities, thereby generating directed movement that reflects realistic patterns such as commuting, migration, and unequal social interaction. The basic reproduction number  is analytically derived using the Next Generation Matrix approach, and the stability of the disease-free equilibrium is established through the Van den Driessche–Watmough method. Elasticity analysis demonstrates that mobility-related parameters substantially increase , while recovery and mortality parameters reduce it, highlighting key factors that drive transmission under directed movement. Numerical simulations across three epidemiological scenarios, defined by the relative ordering of the two cities’ no-mobility reproduction numbers, show that one-way mobility raises the basic reproduction number of the coupled system to approximately 3.99, 2.10, and 1.62, respectively, and consistently elevates infection levels in both cities, even when one city is subcritical in isolation, due to both imported infections and intensified local contact rates. These results suggest that mobility-sensitive interventions, such as movement restrictions on high-mobility populations or social distancing measures in high-transmission cities are essential to prevent directed population flow from destabilizing epidemic control across interconnected regions.
ANALYZING COVID-19 DYNAMICS IN TWO NON-INTERACTING REGIONS THROUGH A STRUCTURED COMPARTMENTAL MODEL Muhammad Afief Balya; Dipo Aldila; Yuni Yulida; Sila Rizqina; Pardi Affandi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 1 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i1.15383

Abstract

COVID-19 is an infectious disease caused by the corona virus. Corona Virus or Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is a virus that attacks the respiratory system. This paper will discuss the effect of the absence of human mobility on the spread of COVID-19. The proposed model consists of ten compartments, including susceptible, exposed, infected (symptomatic and asymptomatic), and recovered individuals in both regions. The model construction in this paper is quite simple, namely it does not involve human mobility at all. This is important because by understanding the characteristics of COVID-19 in a closed population, the spread of COVID-19 locally can be anticipated. Both analytical and numerical approaches are used. The numerical study involves elasticity analysis to identify key influential parameters and autonomous simulations to observe the long-term behavior of the system.
MODEL SEIDR DALAM STUDI PENYEBARAN TUBERKULOSIS: ANALISIS INTERVENSI DIAGNOSIS DAN DAMPAKNYA TERHADAP DINAMIKA INFEKSI Sila Rizqina; Muhammad Afief Balya; Yuni Yulida; Muhammad Ahsar Karim; Hermei Lissa
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 1 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i1.15641

Abstract

Pulmonary Tuberculosis (TB) is a contagious infectious disease caused by Mycobacterium tuberculosis. A person with tuberculosis serves as a source of transmission to the surrounding population. One way to minimize the transmission is through the implementation of effective diagnostic intervention. One approach to understanding the dynamics of TB spread is through the SEIDR epidemiological mathematical model, which includes susceptible, exposed, infectious, diagnosed, and recovered individuals. This study begins by explaining the construction of the SEIDR model, followed by determining the disease-free equilibrium point, the basic reproduction number, local stability analysis of the disease-free equilibrium, and sensitivity analysis. The final step involves conducting numerical simulations and interpreting the results obtained. There are two equilibrium points derived from the model: the disease-free equilibrium and the endemic equilibrium. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one, while the endemic equilibrium point is determined through simulation. Based on the simulation, it is found that the system experiences an outbreak when the basic reproduction number is greater than one. Sensitivity analysis shows that the birth rate has the highest positive influence on the basic reproduction number, while the natural death rate has the highest negative influence on the basic reproduction number. Numerical simulation results show that when transmission is high, the number of diagnosed individuals increases sharply, while the susceptible and exposed populations decrease drastically; conversely, if transmission is suppressed, active cases decline until they are completely eliminated. Therefore, effective interventions are crucial to reduce transmission and to strengthen diagnostic systems in order to achieve TB elimination at the population level
Co-Authors Dipo Aldila Hermei Lissa Muhammad Afief Balya Muhammad Ahsar Karim Pardi Affandi Yuni Yulida Yuni Yulida