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Apri, Mochamad
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Computer Science & IT Electrical & Electronics Engineering Social Sciences

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Optimal control strategies based on extended Kalman filter in mathematical models of COVID-19 Suhika, Dewi; Saragih, Roberd; Handayani, Dewi; Apri, Mochamad
International Journal of Electrical and Computer Engineering (IJECE) Vol 14, No 6: December 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijece.v14i6.pp6300-6312

Abstract

The Omicron variant of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus is an extremely contagious variant that has garnered global attention due to its potential for rapid spread and its impact on the effectiveness of vaccines and non-pharmacological measures. In this paper, we investigate mathematical models involving vaccinated individuals and control functions to analyze how the spread of coronavirus disease 2019 (COVID-19) infection evolves over time. In the process of constructing a mathematical model for COVID-19, there are many parameters whose values are not yet known with certainty. Therefore, the extended Kalman filter method is used as a tool to estimate these parameters in an effort to better understand the dynamics of the spread and evolution of this disease. This method helps align the mathematical model with existing empirical data, allowing us to make more accurate predictions about the course of the COVID-19 pandemic and plan more precise actions to address the situation. Furthermore, an optimal control design is applied to reduce the number of infected individuals by implementing seven strategies involving a combination of health education, vaccination, and isolation controls. The simulation results we conducted indicate that the use of optimal control strategies can lead to a significant decrease in the number of individuals infected with COVID-19.
Mathematical Model for the Growth of Mycobacterium Tuberculosis Infection in the Lungs: Dewanti, Retno Wahyu; Widianto, Wisnu Prasojo; Apri, Mochamad; Nuraini, Nuning; Fakhruddin, Muhammad
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.8

Abstract

In this work, we develop a population dynamics model of Mycobacterium tuberculosis (Mtb), the bacteria responsible for tuberculosis (TB), to evaluate the impact of bacterial competition on infection prevalence. We consider two types of Mtb population growth: The first is caused by bacteria that grow inside each infected macrophage and is believed to be correlated with the number of infected macrophages; The second is that extracellular bacteria grow through self-replication. In this study, we modeled the immune response to Mtb bacterial infection in the lungs using a five-dimensional differential equation system. This model represents changes in the number of healthy macrophages, infected macrophages, activated macrophages cells, extracellular bacterial particles, and naive T cells. Qualitative analysis and numerical results reveal the existence of two equilibrium points: disease-free equilibrium and endemic equilibrium, which represent latent or active tuberculosis based on the number of bacteria. In addition, a sensitive analysis of the model parameters shows that macrophages are not sufficient to control the initial invasion of Mtb. The immune system must therefore employ more complex defense mechanisms to contain Mtb infection, such as recruiting various elements of immune system and forming granulomas.
A Vaccination and Isolation Strategy Based on an Adaptive Sliding Mode Control Design for the COVID-19 Virus (Omicron Variant) in Jakarta, Indonesia Suhika, Dewi; Saragih, Roberd; Handayani, Dewi; Apri, Mochamad
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.2

Abstract

The Omicron variant, identified as B.1.1.529, has been recognized as a variant of concern (VOC) by the World Health Organization (WHO), necessitating continuous monitoring and a proactive response. This study develops a mathematical model to analyze the spread of COVID-19 mutations, considering a population that, despite vaccination, remains susceptible to infection. The model also accounts for key epidemiological factors, including the incubation period, quarantine measures, and various intervention strategies. This study focuses on the epidemiological conditions in Jakarta Province, where the highest number of Omicron cases in Indonesia has been recorded. Real-world epidemiological data related to Omicron in Jakarta were collected between February 6, 2022, and May 6, 2022. Model parameters were estimated using genetic algorithm optimization. A significant challenge in epidemic modeling is the uncertainty of parameters, which can substantially affect the effectiveness of control measures. To address this challenge, an adaptive sliding mode control approach is introduced, allowing dynamic adjustments to parameter variations without requiring precise parameter estimation. This approach maintains system stability by enforcing a predefined sliding surface, making it inherently robust against uncertainties. The main goal of this approach is to gradually minimize infections attributed to the initial COVID-19 strain and the Omicron variant, while simultaneously decreasing the count of susceptible individuals by ensuring the system follows a specified reference trajectory. Additionally, an adaptive mechanism is implemented to account for unknown variations in the system using the Lyapunov stability theorem. Numerical simulations illustrate that adaptive sliding mode control significantly improves epidemic management, reducing infections by 92.8% for the original strain and by 96.87% for the Omicron variant when compared to an uncontrolled scenario. Furthermore, the basic reproduction number (R0) is lowered by 85.92%, confirming the efficiency of adaptive sliding mode control in mitigating the outbreak. Moreover, this study incorporates a cost-effectiveness analysis to assess the viability of various vaccination and isolation strategies. The findings contribute to epidemiological research by offering valuable insights for policymakers in designing effective and resilient intervention strategies for epidemic management.
Analyzing Mask-Wearing Decisions Using Game Theory and the SIR Model with a Replicator Equation in Post-Pandemic Situations Nasution, Yuki Novia; Rizqo, Muhammad Abyan; Nuraini, Nuning; Apri, Mochamad; Susanto, Hadi
Communication in Biomathematical Sciences Vol. 9 No. 1 (2026)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2026.9.1.1

Abstract

During the COVID-19 pandemic, many countries implemented policies on using masks to control the outbreak. This policy has been relaxed in almost all countries, after which. Respiratory disease outbreaks re-emerged in several countries, including Indonesia. This article presents a game-theoretic model of mask use by the community during the spread of the disease. Both the effectiveness of masks in preventing the spread of the disease and the proportion of the infected population are included in the payoff calculation. The model is combined a with the Susceptible-Infectious-Recovered (SIR) epidemic model with the replicator equation. The model is also evaluated under Nash equilibrium conditions. Simulations are carried out to effect of mask-wearing behavior on the incidence of acute respiratory infection in Jakarta. The results show that an individual's decision to use a mask is directly proportional to mask users. To reduce the number of infections, more than 10% of the population need to wear masks when the disease first appears. In the Nash equilibrium, we obtain a threshold value of the infected population at which the players decide not to use the mask. The results suggest that when respiratory infectious diseases emerge, governments must implement a stringent mask policy to control their spread and reduce infections.
Co-Authors Dewi Handayani Hadi Susanto Nuning Nuraini Retno Wahyu Dewanti Rizqo, Muhammad Abyan Suhika, Dewi Syamsiar, Syamsiar Widianto, Wisnu Prasojo Yuki Novia Nasution, Yuki Novia