Research Papers of
BS Applied Mathematics 4-2

Social Media Addiction is a progressive issue within society as social media become a relevant tool in our daily lives. This study presents a mathematical modeling approach to understand the dynamics of social media addiction with the optimal control measures and the influence of the additional Abstinence compartment. The mathematical model integrates the interactions between Susceptible, Exposed, Addicted, Abstained, Recovered, and individuals who quit. In the study, Ordinary Differential Equations were formulated to interpret the SEABRQ model dynamics of social media addiction. Also, Lipschitz condition was used to evaluate the existence and uniqueness of the model, followed by two theorems to prove the positivity and boundedness of the solution. Moreover, the eigenvalues of the model's Jacobian matrix will be calculated in order to determine the stability of the disease-free equilibrium while Sensitivity Index Formula is used to check which parameter is the Reproductive Number Sensitive to. Lastly, the existence of optimal control is used to check if the control measures can be used within feasible limits which is shown by the results of the numerical simulation where it emphasizes the effect of additional intervention along with appropriate control measures in minimizing social media addiction within the population.

Keywords: social media, addiction, behavior management, optimal control measures, addiction intervention

Floods in high-risk areas can increase the spread of typhoid fever by contaminating water sources with sewage and harmful bacteria. People living in high flood-risk areas should consume only clean food and water to prevent contracting typhoid fever. This research will explore the impact of living in high flood-risk areas in Metro Manila on the rising cases of typhoid fever, using a mathematical model based on the SEIR (Susceptible-Exposed-Infectious-Recovered) model. We also analyze and develop ordinary differential equations in the model. This research addresses the formulations and testing procedures, including positivity, boundedness, existence, uniqueness, equilibrium, stability, optimal control, sensitivity analysis, model simulations and simulation by the use of matlab. The research is not based on medical information but forecasts how the disease spreads especially in high flood-risk areas.

Keywords: high flood-risk areas, low flood-risk areas, ordinary differential equations, SEIR model, typhoid

Asthma is a chronic respiratory condition significantly influenced by factors such as genetic predisposition, obesity and pollution. This study develops a nonlinear mathematical model that demonstrates the development of asthma due to obesity and environmental pollution among obese and non-obese individuals. The model is formulated using Ordinary Differential Equations (ODEs) to analyze the dynamics of asthma development. The theoretical analysis reveals that the asthma-obesity compartmental model, when transformed into ODEs, has solutions that are unique, positive, and bounded within the specified parameters for any non-negative time t. The equilibrium test and stability analysis were conducted to understand the long-term behavior of asthma prevalence under varying conditions and to gain deeper insights into the model’s dynamics. The researchers also investigated the effect of control strategies such as proper diet and exercise and awareness campaigns about combating environmental pollution to reduce the risk of asthma incidence. Numerical simulations demonstrate that integrated control measures can substantially reduce the incidence of asthma development, emphasizing the importance of addressing obesity and pollution simultaneously.

Keywords: asthma, obesity, environmental pollution, mathematical modeling, compartmental model, optimal control

This research develops an SVEIR (Susceptible, Vaccinated, Exposed, Infected, Recovered) model to study the transmission dynamics of tuberculosis (TB) in the Philippines, with a focus on vaccination and immunity-waning delay. The Lipschitz condition confirms the model's existence and uniqueness, while two theorems establish solution positivity and boundedness. The equilibrium analysis of the model suggests that disease elimination is possible under favorable conditions. Furthermore, the eigenvalues of the Jacobian matrix are computed to assess the stability of both the disease-free and endemic equilibria. The Sensitivity Index Formula is used to determine which parameter significantly impacts the Reproductive Number. The Sensitivity Index Formula is utilized to determine which parameter significantly impacts the Reproductive Number. The results highlight the necessity of increasing vaccination coverage to reduce TB transmission, especially among at-risk populations. Recommendations include bolstering vaccination initiatives and enforcing strict isolation measures to enhance TB control strategies and improve public health outcomes in the Philippines.

Keywords: tuberculosis, transmission dynamics, SVEIR model, vaccination, immunity-waning delay, equilibrium analysis, sensitivity analysis. 

Eating disorders are non-communicable diseases that can be fatal and they have become a major health issue. A compartmental model was proposed in this paper for the study that focused on the dynamics of media influence and peer pressure on the onset of eating disorders. Therapy, medicine, and an individual's willingness were used as they are the most common and available treatment strategies for individuals with eating disorders.

With the use of the Jacobian Matrix, the stability of the model was proven in both disease-free and endemic equilibrium. The sensitivity was also calculated that showed that the most sensitive parameter is the peer pressure influence on individuals being anorexic. Furthermore, the paper determined the optimal control solution for the corresponding mathematical model and ordinary differential equations that helped in the controlling or decrease of anorexic, bulimic, and binge eaters as well as maximizing the effectiveness of the treatments. The numerical simulation was made with the use of MATLAB programming that shows the results of applying the optimal control strategies in the model. 

Keywords: optimal control, sensitivity analysis, compartmental model, anorexia, bulimia, binge eating, media influence, peer pressure, therapy, medicine, individual's willingness, non-communicable disease