UNESA Gubes Develops Mathematical Modeling to Understand the Spread of Infectious Diseases

"Unesa.ac.id. SURABAYA – Born and raised in the City of Heroes, Prof. Abadi hails from a simple family that always emphasized the importance of education as a path to change. His perseverance and passion for science have led him to become a professor of applied mathematics (dynamical systems) at Universitas Negeri Surabaya (UNESA) on October 29, 2024.

At his inauguration, he delivered a scientific speech entitled "Dynamical Systems and Their Applications in Mechanics, Infectious Disease Spread, and Population Interaction (Mathematical Modeling and Analysis Studies and Their Interpretation)," applying mathematics to various fields.

He explained how dynamical systems are mathematical tools that can be used to understand the changes of various phenomena in real life. Dynamical systems are mathematical models that describe how a phenomenon evolves over time.

According to him, through this mathematical model, understanding of physical, biological, and economic changes can be identified and analyzed more accurately.

In his research, he developed an auto-parametric system model to study stability in weakly vibrating systems. This system consists of two subsystems, with one subsystem as an oscillator or primary system, while the other subsystem acts as a secondary system connected non-linearly.

"This model allows the secondary system to remain stable when the primary system oscillates, creating an auto-parametric mechanism that is divided based on the cause of excitation such as external force, parametric, and self-excitation," he explained."

"Through mathematical modeling and heterocline cycle graphs, he demonstrated that the solutions of this system are bounded and stable through a process known as Hopf bifurcation. Stability in this autoparametric system is important to ensure the boundedness of solutions, meaning that the system reaches equilibrium despite being influenced by oscillations.

Not only that, Prof. Abadi also developed a mathematical model to understand the spread of infectious diseases, particularly measles. The developed model modified the classic SIR (Susceptible-Infected-Recovered) model from 1927 by considering vaccination and hospitalization actions.

This modified model, called the SIHR (Susceptible-Infected-Hospitalized-Recovered) model, shows how vaccination and treatment for measles patients can significantly suppress the spread of the disease.

"From the simulation results we have conducted, it can be concluded that vaccination and hospitalization are effective in suppressing the rate of measles transmission, which supports health policies in controlling infectious diseases," he explained.

His study was also applied to population interactions through the Lotka-Volterra predator-prey model by considering the variability of environmental carrying capacity. He included fluctuations in environmental carrying capacity in this model because, in reality, this carrying capacity often changes.

This model shows that under certain conditions, predator and prey populations can reach a stable ecosystem equilibrium.

"The stable periodic solutions we obtained show that predator, prey, and resource populations can coexist at a certain equilibrium. This is important in conservation efforts as it shows the potential for the sustainability of resources and populations in ecosystems," he added.

He hopes that the results of his research can provide real benefits in the fields of health, technology, and environmental sustainability, and encourage the younger generation to continue innovating. [*]

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Reporter: Muhammad Dian Purnama (FMIPA)

Editor: @zam*

Photo: UNESA Public Relations Team"

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