Research Papers of
BS Applied Mathematics 4-1

Diabetes is a major health concern in the Philippines, ranked as the fourth leading cause of mortality in the country. It is associated with risk factors such as obesity and smoking, particularly in cases of type 2 diabetes. This study adapts a deterministic model of obesity and diabetes, incorporating smoker and obese-smoker compartments to examine their dynamics. The solutions of the model were analyzed for positivity, boundedness, existence and uniqueness. We identified equilibrium points and proved the stability of the disease-free equilibrium point with the help of the basic reproduction number. Sensitivity analysis was performed using the partial rank correlation coefficient and Latin hypercube sampling with Python to assess the impact of parameters associated with obesity, smoking, and diagnosed diabetes on the basic reproduction number. The most sensitive parameters were the development rate of diabetes in obese individuals, the recruitment rate of healthy individuals, and the effective contact rate. Pontryagin's Maximum Principle was employed to determine optimal control strategies for the system, aiming to reduce the incidence of diabetes. Numerical simulations using the Runge-Kutta fourth order method in MATLAB validated the model. The results demonstrate that implementing optimal control strategies effectively reduces the populations in the Obese, Smoker, Obese-Smoker, and Diabetic compartments while increasing the Healthy population.

Keywords: type 2 diabetes, obesity, smoking, deterministic model, sensitivity analysis, optimal control, pontryagin’s maximum principle, runge-kutta

Rabies is a deadly zoonotic disease transmitted primarily through bites or saliva from infected animals. In the Philippines, dogs are the principal reservoirs for rabies, accounting for most human cases. This article presents a delay differential equations model to evaluate the impacts of control measures and the incubation period (time delay) on the dynamics of rabies transmission between humans and dogs in the Philippines. The study finds that time delay affects the persistence of rabies. To mitigate rabies spread in the Philippines, the model suggests implementing both human and dog vaccinations along with controlling the annual birth rate of puppies. Sensitivity analysis indicates that in human populations, increasing the dog vaccination rate and reducing puppy births are particularly effective. For dog populations, both vaccination and controlling puppy births are equally impactful for rabies management. Theoretical results and control strategies are illustrated through numerical experiments to support these findings.

Keywords: rabies virus, time delay, vaccination, birth control of puppies, transmission dynamics, dde

This study examines the impact of the Philippine Road Safety Action Plan (PRSAP 2023-2028) on reducing drunk driving accidents in Metro Manila. Specifically, it looks at the plan’s efforts to enhance road user safety and improve post-crash response. By utilizing a mathematical model inspired by El Youssoufi’s compartmental model, and basing the values from MMARAS and WHO, the research delves into the behaviors associated with drunk driving and their effects on road safety. Using analysis, the researchers identified that the most sensitive parameter to the reproduction of the drunk drivers is the γ or the drunk drivers who caused an accident and quitted drunk driving. The results suggest that the PRSAP’s comprehensive approach, the road user behavior initiatives, and post-crash care, which are the fourth and fifth pillar of the plan, respectively holds promise for significantly reducing drunk driving accidents. The plan’s success, however, largely hinges on effective implementation and adherence by 2028. This study offers valuable insights into optimizing control measures where maximizing the effectiveness of the plan while minimizing the cost-related difficulties and emphasizes the need for heightened public awareness and stricter enforcement of traffic laws to meet the plan’s goals. It underscores the crucial role of data-driven policymaking in enhancing road safety and reducing alcohol-related road accidents in Metro Manila.

Keywords: Philippine Road Safety Action Plan (PRSAP), drunk driving accidents, road user safety, post-crash response, road user behavior initiatives

Rice Tungro Virus Disease, recognized as a cancer disease, is one of the most economically damaging vector-borne plant diseases in tropical countries like the Philippines. It is caused by two viruses: Rice Tungro Bacilliform Virus and Rice Tungro Spherical Virus which are transmitted by Nephotettix virescens. Typically, farmers use cultural and chemical controls to manage the spread of the disease. Blas developed an RTVD transmission model in 2016 that incorporates the characteristics of the two viruses, and in 2017, the researchers expanded the model by including roguing, a cultural control method in which symptomatic rice plants are uprooted from the fields. 

The primary goal of this research is to modify the previous roguing model by proposing a system that combines periodic application of cultural and chemical control strategies. To achieve a more realistic and practical approach, the model will be extended by using impulsive differential equations. The models were tested for well-posedness using standard mathematical methods, while Jacobian matrices and Floquet theory for impulsive models were utilized to examine the local stability of the disease-free equilibrium point and periodic solution. Python's Latin Hypercube Sampling was used to perform sensitivity analysis on the continuous model, and numerical simulations were carried out using Python's RK45 ODE solver. The numerical findings suggest that the periodic hybrid control model led to a more viable and accurate approach compared to the continuous model. Results also show that roguing every 15-day interval and insecticide spraying every 30-day interval is the optimal strategy for mitigating the disease. Moreover, the simulations with a roguing effectiveness rate of 1 and insecticide effectiveness rate of 0.7 displayed ideal results, whereas effectiveness rates of 0.4 and 0.2 for roguing, and 0.6 for insecticide yield a more optimal approach with consideration of practicality.

Keywords: impulsive, continuous, control model, rice tungro virus disease

Studies relating to rumor propagation is relevant up to this day since the spread of fake news is a huge concern today, especially with the help of technology. Recent study also shows that rumors with positive sentiments have reached 61.44% more people and have 37.58% more lifetime when spreading compared to those who have negative sentiments (Pröllochs et al., 2021). In this study, the rumor propagation is visualized using epidemiological model by considering the rumor as the "virus" and included two additional compartments: the Positively Influenced Emotion compartment (M+) and the Negatively Influenced Emotion compartment (M-). The researchers used MATLAB programming language to simulate the rumor propagation with the influenced of positive and negative emotions, the results shows that by introducing control strategies, the amount of population in the Infected/Marites compartment (M) and M+ compartments could be decreased, and increased the population in M- and Stifler (S) compartments. Thus, this study concludes that informing people about the right information and quick action towards rumors will greatly affect the spread and help in decreasing the possible damage that it could have done to the society.

Keywords: rumor propagation, optimal control theory, emotion-influenced, MATLAB, ODE, mathematical modeling, epidemiological model

In the Philippines, the pervasive issue of illegal drug addiction presents formidable challenges, particularly to the country's social and economic well-being. This study highlights the significant role of drug pushers in this problem. Its primary objective is to develop a compartmental model that integrates the drug pusher population and to investigate the effects of control strategies to mitigate drug addiction. The researchers employed three different strategies: Preventive Education and Advocacy Programs, Anti-Illegal Drug Police Operations, and Aftercare Program. To understand the local behavior of the proposed model, R0 was calculated. The sensitivity analysis employed is a combination of Partial Rank Correlation Coefficient (PRCC) and Latin Hypercube Sampling (LHS) methods. The analysis identified the escalation rate of drug users due to the presence of drug pushers, rehabilitation rate, escalation rate of drug pushers, and law enforcement as the most sensitive parameters. To characterize the optimal control solutions, Pontryagin’s Maximum Principle was applied. Numerical simulations were conducted using MATLAB R2024a ‘ode45’ function with Runge-Kutta Method. Findings suggest that simultaneous implementation of all control variables yields the most substantial reduction in drug users, emphasizing the importance of comprehensive intervention strategies in combating drug addiction.

Keywords: illegal drug addiction, drug pushers, sensitivity analysis, optimal control

Soil-Transmitted Helminth (STH) is classified among neglected tropical diseases and is prevalent worldwide. Despite efforts by the Department of Health (DOH) to eliminate STH by following the World Health Organization’s (WHO) strategy of halting transmission through mass drug administration, the infection remains endemic in certain areas of the Philippines. This study proposes a model for the transmission dynamics of soil-transmitted helminths and introduces an optimal control strategy. The control parameter considered is treatment coverage ui. Unlike previous models, this new approach integrates optimal control strategies including health education, mass drug administration, and WASH implementation. Researchers also examine seasonal variations to determine the most effective timing for implementing treatment coverage. Local dynamics of the proposed model are assessed through the calculation of R0. Sensitivity analysis using the partial rank correlation coefficient (PRCC) identifies key parameters such as mortality rate, disease induced death rate, carrying capacity of parasite to the environment, recovery rate, and clearance rate of parasite as most critical. An optimal control strategy is derived to minimize the numbers of susceptible, exposed, and infected individuals, as well as the parasite population. Simulation results demonstrate that maintaining high treatment coverage, especially timed with low egg and larval counts, is crucial for reducing STH infections over time. The study recommends integrating continuous health education into school curricula and aligning MDA with optimal seasonal periods to enhance the effectiveness of control strategies. These insights are vital for public health initiatives aiming to sustainably control and reduce STH infections.

Keywords: soil-transmitted helminth, seasonal variation, sensitivity analysis, optimal control, runge-kutta, routh-hurwitz, ordinary differential equation