Communication in Biomathematical Sciences

Optimal Management of Nitrogen Pollution

Worku Bitew

Water quality and invasion of weeds due to nutrient eutrophication have been a concern in major lakes and coastal areas. Scholars have advocated the cultivation of some species of shellfish as a new potential to facilitate the bioremediation of the polluted environment due to excessive nutrients. In this paper, our objective is to determine the optimal area that must be dedicated to shellfish aquaculture relative to other fisheries activities and the performance of wild catch. The optimal size also depends on the effort outside the water body to control pollution from the point source. We set up transition equations that describe the system’s state based on pollution reduction efforts, nitrogen concentration level, and the size of shellfish cultivation. We show that the impact of the nitrogen concentration level in the habitat can be minimized by allocating optimal management efforts to reduce nitrogen waste from the source and setting aside an area for shellfish cultivation. We found the optimal steady-state solutions and analyzed the optimal solutions based on biological and economic parameters.

Mathematical modelling of malaria transmission dynamics with resistant humans

Obiora Collins

Malaria is a life-threatening disease especially among individuals that have little or no resistance to the disease. A mathematical model that incorporates an individual's ability to resist malaria infection is consider to study the dynamics of malaria and the effects of possible resistance on these dynamics. Preliminary analyses reveal that the dynamics can undergo a backward bifurcation induced by the ability of individuals to resist malaria. By fitting the model to recorded data on the incidence of malaria in Nigeria important parameters associated with the disease dynamics are estimated. Using these estimated parameters, the basic reproduction number is calculated, future disease dynamics simulated, and the effect of the ability of individuals to resist malaria infection explored. The results indicate that the possibility of eradicating malaria infection is largely dependent on the ability of individuals to resist malaria infection.

A New Modified Mathematical Model and Numerical Analysis of SITR Dynamics for COVID-19

Mehmet KOCABIYIK

The mathematical SITR model (Susceptible-Infectious-Treatment-Recovered) for COVID-19 has been extensively studied involving discretization techniques and detailed numerical analysis. The Nonstandard Finite Difference (NSFD) method has been employed for discretization enhancing the accuracy of the model's predictions. The equation system has been modified to explore various scenarios and improve predictive capabilities. Equilibrium points of the model have been rigorously analyzed to understand stability and epidemiological outcomes. Additionally numerical simulations have been conducted to validate the model's predictions against real-world data. These advancements have significantly bolstered the model's analytical power stability assessment.

Discrete Mathematical Model of Fast Food Consumption : Control Approach

Hicham BENAISSA

We deal with a time-discrete mathematical model PLSCQ to describe the interactions between the behav- iors of categories of fast food consumers, namely potential fast food consumers (P ), individuals who are moderate fast food consumers (L), individuals who consume excessive fast food (S), obese patients (C), and patients who stop fast food consumption (Q). We also emphasize the significance of educational programs, healthy eating campaigns, and treatments to reveal the best strategy to decrease the population of excessive fast food consumers and obese patients and maximize the number of patients with obesity who stop or recover from fast food. We use three controls, representing media and educational awareness programs for potential fast food consumers, healthy eating campaigns for excessive fast food consumers, and treatment for obese patients. We employ discrete-time Pontryagin maximum principle to define optimal controls. The optimality system is then numerically solved using Matlab, demonstrating the effectiveness of the optimization strategy through the results obtained.