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All Journal Communication in Biomathematical Sciences Jambura Journal of Biomathematics (JJBM)
Pietrus, Alain
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Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Social Sciences

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Mathematical model with fractional order derivatives for Tuberculosis taking into account its relationship with HIV/AIDS and Diabetes Moya, Erick Manuel Delgado; Pietrus, Alain; Oliva, Sergio Muniz
Jambura Journal of Biomathematics (JJBM) Volume 2, Issue 2: December 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v2i2.11553

Abstract

In this paper, we present a mathematical model for the study of resistance to tuberculosis treatment using fractional derivatives in the Caputo sense. This model takes into account the relationship between Tuberculosis, HIV/AIDS, and diabetes and differentiates resistance cases into MDR-TB (multidrug-resistant tuberculosis) and XDR-TB (extensively drug-resistant tuberculosis). We present the basic results associated with the model and study the behavior of the disease-free equilibrium points in the different sub-populations, TB-Only, TB-HIV/AIDS, and TB-Diabetes. We performed computational simulations for different fractional orders (α-values) using an Adams-Bashforth-Moulton type predictor-corrector PECE method. Among the results obtained, we have that the MDR-TB cases in all sub-populations decrease at the beginning of the study for the different α-values. In XDR-TB cases in the TB-Only sub-population, there is a decrease in the number of cases. XDR-TB cases in the TB-HIV/AIDS sub-population have differentiated behavior depending on α. This knowledge helps to design an effective control strategy. The XDR-TB cases in diabetics increased throughout the study period and outperformed all resistant compartments for the different α-values. We recommend special attention to the control of this compartment due to this growth.
A Novel Mathematical Model for Overweight, Obesity, and Their Impact on Diabetes and Hypertension Delgado Moya, Erick Manuel; Rodriguez, Ranses Alfonso; Pietrus, Alain; Bernard, Severine
Communication in Biomathematical Sciences Vol. 8 No. 2 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.2.5

Abstract

In this paper, we present a new mathematical model describing the dynamics of overweight and obesity and their impact on diabetes and hypertension. In constructing the model, we consider negative and positive interactions among individuals with normal weight, overweight, and obesity, as well as social factors influencing overweight and hypertension diagnoses. As a novel contribution to transmission dynamics, we interpret the basic reproduction number from two perspectives: negative and positive interactions. Focusing on parameters linked to social factors and their health impact, we present theoretical results characterizing their influence on the basic reproduction number and compute corresponding sensitivity indices. Additionally, we perform a global sensitivity analysis of model parameters using first- and total-order Sobol’ indices with various methods and sampling techniques, concluding that parameters associated with social factors are among the most influential. We conduct computational simulations of the basic reproduction number and model’s compartments to examine the influence of social-factor parameters on overweight and hypertension. Our findings indicate the need to explore strategies to prevent the rise of overweight, obesity, and diabetes in the population. Social factors associated with overweight and hypertension diagnosis have a substantial impact on the progression of these dynamics. Recognizing this influence enables the identification of the most vulnerable groups and the design of more precise and effective interventions.
Co-Authors Bernard, Severine Delgado Moya, Erick Manuel Moya, Erick Manuel Delgado Oliva, Sergio Muniz Rodriguez, Ranses Alfonso