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Optimal control and stability analysis of influenza transmission dynamics with quarantine interventions
(2025-08-01)
Lamwong, Jiraporn
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Pongsumpun, Puntani
Seasonal flu results from infection by influenza viruses of either type A or B. Common symptoms include a rapid rise in body temperature, coughing, headaches, muscle and joint aches, throat discomfort, and nasal congestion. This research addresses the need for effective modeling and control of seasonal influenza, which remains a significant health concern globally due to its high transmissibility and potential to cause severe illness. Current approaches to understanding and managing influenza focus on various mathematical models exploring transmission dynamics and control strategies. This study contributes to the field by introducing a Susceptible-Exposed-Infectious-Quarantined-Recovered (SEIQR) model, which uniquely incorporates quarantine as a key intervention, reflecting realistic disease management practices. The methodology utilized involves formulating the SEIQR model to simulate the transmission of influenza and analyze its stability. The stability of both the disease-free and endemic equilibrium points is examined using Lyapunov functions and LaSalle’s invariance principle, ensuring the rigorous validation of the model's behavior. To enhance the model's utility, optimal control theory is applied, incorporating control variables such as vaccination, social measures, and treatment for both infected and quarantined populations. The application of Pontryagin’s Maximum Principle enables the derivation of optimal control strategies that balance epidemiological impact with cost-effectiveness. Numerical simulations provide key results that demonstrate the efficacy of control interventions. Specifically, scenarios implementing control measures reveal a significant reduction in the peak and overall spread of infections. The analysis of different control policies indicates that a combined approach—employing both vaccination and social distancing—is the most effective for curbing the spread of influenza. Sensitivity analysis further underscores the critical influence of parameters like quarantine rate and infection rate on the basic reproduction number, R<inf>0</inf>, reinforcing the importance of targeted interventions. The study’s findings emphasize the importance of timely and multifaceted control measures for achieving the global asymptotic stability of the influenza model. The implications suggest that integrated strategies, particularly those involving vaccination and social controls, are crucial for public health policy to manage and prevent influenza outbreaks effectively. Future research could expand the model to include demographic variations, virus mutations, and interactions with other respiratory diseases, enhancing its predictive power and practical relevance for disease control.
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A mathematical model of water pollution measurement in a stream using a collocation method with a higher order Legendre polynomial
(2025-08-01)
Thongtha, Kaboon
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Pochai, Nopparat
In environmental research, challenges with water contamination assessment are generally prevalent. Through data collection, pollution levels in a system may be determined. This is quite challenging and involved; the measurements of what was measured vary from one point to another in every location. The governing equations for a uniform flow pollution dispersion model are used in water quality modeling. The advection-diffusion-reaction equation used in water quality model-ing for a uniform flow stream is a stable pollution dispersion model. This study presents a one-dimensional mathematical model for measuring stream water quality by collocation higher order Legendre polynomial functions. A water pol-lutant concentration can be approximated using the collocation method. A related water quality quantification method may also be employed with the suggested mathematical simulation to approximate the solution.
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A simple mathematical model for assessing water quality in a closed-system shrimp farm
(2025-08-01)
Thongtha, Kaboon
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Pochai, Nopparat
The problem of wastewater from shrimp farming affects the environment, both in terms of wastewater discharge and soil deterioration. Wastewater management is also quite expensive for the production costs of shrimp farmers. Therefore, the approach to using shrimp farming technology in closed-system farms is proposed, which reduces wastewater discharge into the environment and reduces the cost of wastewater treatment for farmers. This research presents a simple mathematical model for assessing water quality in such closed-system shrimp farms. The method for determining various parameters for determining the mathematical model is presented. The model solution is estimated by the Runge-Kutta method of the fourth order. This research simulates the situation to compare the different parameter values in each situation, which affect the level of water quality in closed-system shrimp farms at different times. The research found that the initial water quality, the rate of chemical reaction of pollutants, the rate of pollution formation, the rate of pollution decomposition, the rate of decrease in pollution concentration due to water circulation between the farm and the water treatment pond, and time all affect water quality. The results from the calculation can help closed-system shrimp farmers know the trend of pollution concentration changes in closed-system shrimp farms in order to find ways to develop techniques for improving water quality.
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Mathematical modeling and stability of SARS-CoV-2 transmission dynamics among domestic tourists in Thailand
(2025-02-01)
Sungchasit, Rattiya
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Pongsumpun, Puntani
The defined epidemiological model system explaining the spread of infectious diseases characterized with SARS-CoV-2 is analysed. The resulting SEIQR model is analysed in a closed system. It considers the basic reproductive value, the equilibrium point, local subclinical stability of the disease-free equilibrium point and local subclinical stability of the endemic equilibrium point. This is examined and the asymptotic dynamics of the appropriate model system are investigated. Further, a sensitivity analysis supplemented by simulations is prepared in advance to impose how changes in parameters involve the dynamic behaviours of the model.
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A Numerical Simulation of the Kratom Plant Growth Model While Treated by a Specific Nutrient Using an Explicit Finite Difference Method
(2025-01-01)
Krongsamsri, Pitchayapa
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Komthong, Nontalee
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Yammeng, Jidapa
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Chaichuay, Chinda
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Boonchom, Banjong
Kratom refers to both Mitragyna speciosa, a tree native to Southeast Asia, and products manufactured from its leaves sold as herbal supplements. Kratom leaves contain a range of chemical compounds known as bioactive alkaloids, which have physiological effects. A mathematical model of the Kratom plant under a particular nutritional treatment will be provided in this research. Also, the methods for setting the initial condition and boundary condition will be presented. Also, as the plant grows, the solution's domain shifts every time. Techniques for adjusting the specific nutrient's physical parameters are also provided. With the use of an explicit finite difference method, the solutions are approximated. The specific nutritional concentrations are calculated for each height level. As shown, the specific nutrient will spread from the root to the apex of the trunk. The nutrient has the capacity to stimulate the growth of the Kratom. The specific nutrient concentration along the trunk may be measured using the proposed mathematical model as the Kratom plant grows each day. A proposed numerical model with a specific nutrient can be used to develop a precise model, such as a one-dimensional model of branches and foliage. It would be more captivating if the plant nutrients indicated here were researched for their ability to accelerate the growth of large or medium-sized Kratom plants. In conclusion, the study shows that calcium dihydrogen phosphate monohydrate may be useful as a growth promoter for Kratom plants and suggests a way to measure its effects quantitatively.
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A Mathematical Model for Evaluating the Risk of Airborne Infection Among Bus Passengers Using Ventilation Systems
(2024-01-01)
Sooknum, Jenjira
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Pochai, Nopparat
Carbon dioxide from human breath contributes significantly to airborne diseases. Breathing can expose us to usually dangerous airborne infections, which rapidly spread. By using a bus, there is a chance of contracting an infection. This study takes into account a mathematical model of airborne infection caused by human breath. The purpose of this research is to evaluate the probability that passengers in a bus with ventilation systems may well get an airborne infection. The model can be divided into five submodels, such as an exhaled air concentration measurement model for a bus with a variable number of passengers, the volume fraction of exhaled air model, the concentration of airborne infectious particles model, the number of airborne infectious particles model, and the risk of airborne infection model. The model’s solution might be used to determine the probability that susceptible people will get an airborne infection. An explicit forward-time centered-space finite difference method is used to approximate the solution. In order to reduce the risk of airborne infection and improve ventilation, the provided mathematical models were used to assess the risk of airborne infection among bus passengers using ventilation systems. Better air quality control that balances the number of passengers allowed to travel on a bus will be among the ventilation’s main advantages.
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Mathematical modelling of roselle seeds (Hibiscus sabdariffa L.) drying kinetics
(2023-08-01)
Thuy, N. M.
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Tram, N. B.
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Cuong, D. G.
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An, L. T.
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Duy, H. K.
Roselle seeds (Hisbiscus sabdariffa L.) are among the seeds that are high in nutrients and can be useful in several applications. Through the drying process, the seeds can be preserved for a long time. The roselle seeds were oven-dried at different temperatures 55, 60, 65 and 70°C, giving different outlet values for yield and final moisture. A total of five empirical mathematical models (Newton, Henderson and Pabis, Logarithmic, Diffusion approach and Page) were selected to describe and compare the drying characteristics of roselle seeds at respective drying temperatures. The adequately suitable drying temperature was found to be 70°C with a drying time of 4 hrs. The effective moisture diffusivity was calculated using the Fick diffusion equation. The results showed that the moisture content of the seeds gradually decreased with time. The effective diffusivity coefficient of moisture transfer varied from 5.4262×10-10 to 1.074×10-9 m2/s over the temperature range investigated. Mathematical models were fitted to the experimental data and by statistical comparison, the Page model represented drying characteristics better than the other equations with the highest R2 (0.998) and the lowest values of χ2 (0.00033) and RMSE (0.00023) observed for drying air temperature of 70°C. The dependence of moisture diffusivity on temperature was described by the Arrhenius equation, with the estimated activation energy being 43.08 kJ/mol within 55 to 70°C. Based on the selected model, it is possible to predict the moisture change during the drying of roselle seeds and thereby better control the process.
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A Mathematical Model for the Evaluation of Airborne Infection Risk for Bus Passengers
(2023-03-01)
Sooknum, Jenjira
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Pochai, Nopparat
Human breath emits a lot of carbon dioxide, which contributes a lot to airborne infections. Airborne infections spread speedily, and breathing can expose us to life-threatening airborne infections. There is a risk of infection if people are traveling by bus. A mathematical model of carbon dioxide concentration measurement due to human breath is proposed in this research. The focus of this research is to determine the amount of carbon dioxide produced by bus passengers. The model's solution is approximated using an explicit finite difference technique. The model solution can be used to determine how much time passengers are willing to spend on the bus while carbon dioxide levels are kept under control. Furthermore, mathematical models were utilized to quantify the risk of air infection among bus passengers with ventilation systems, in order to reduce the risk of air infection and increase ventilation. The proposed air quality model was found to be in good agreement in that it allows us to know the balance between the number of passengers allowed to sit on the bus while managing the risk of airborne infection, carbon dioxide concentration, and ventilation system potential. A significant advantage of the ventilation will be better air quality control that balances the number of passengers permitted to ride on a bus
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Mathematical Model of Wind Turbine Simulator Based Five Phase Permanent Magnet Synchronous Generator Supplying Non-Linear Loads
(2023-01-01)
Meesuk, Peerawat
;
Kinnares, Vijit
This paper propose the mathematical model simulation of a wind turbine power generation system using MATLAB/SIMULINK. The 5-phase synchronous permanent magnet generator is a device that converts mechanical energy from wind turbines into electrical energy. The electrical power is passed through a non-linear load as a rectifier using 10 diodes per 5-phase for further conduction through the inverter and grid connection. The simulation results show the voltage output from the generator in all 5 phases, the rotor speed, stator current, and electromagnetic torque. When adjusting the speed according to the characteristics of the wind that is fed to the wind turbine, the rotor speed is adjusted. Stator current, torque and voltage also change.
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A Non-Dimensional Mathematical Model of Shoreline Evolution with a Groin Structure Using an Unconditionally Stable Explicit Finite Difference Technique
(2022-01-01)
Manilam, Surasak
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Pochai, Nopparat
Abstract—Coastal erosion is a natural phenomenon that occurs when sediment transport away from the coast is not countered by the formation of new material on the shoreline. This is indeed a problem that is driving the erosion of coastal areas. A sea wall and a groin were created to prevent coastal erosion and floods. The future topography of the beach is being investigated using shoreline evolution analysis. Erosion, accretion, and sea level changes are basic stages that have a significant impact on the coastal structure. A qualitative analysis of the model coastal behavior in relation to the controlling process is required to research beach erosion and beach deposition. When stated in terms of non-dimensional variables, all are mathematically equivalent. In general, the models do not have to be dimensionally different. Those might just be modifications of the same problems. One can solve a wide range of models with a single solution to the related nondimensional equation. In this research, we provide a governing equation when a groin is introduced to a one-dimensional shoreline growth model. A non-dimensional shoreline evolution model with a groin structure model is provided. The model now has the ability to manipulate physical parameters. When groin structural effects are present, the initial condition setting method and boundary condition approaches are also given. To approximate the incremental model in each year, the forward time-centered space technique and the unconditionally stable Saulyev finite difference methods are used. The Saulyev finite difference approach can handle numerical solutions in almost any scenario since the stability requirements are not restricted. The Saulyev finite difference technique can be very useful for computing a practical conceptual design of shoreline evolution since the number of grids has increased. The numerical models offered provide a viable simulation for evaluating long-term coastal development. The proposed modeling may be used to forecast the effectiveness of constructing a groin system on a local beach.

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