Communication in Biomathematical Sciences

A MATHEMATICAL MODEL OF THE GLUCOCORTICOID EFFECTS FOLLOWING PREVENTIVE ADMINISTRATION IN A MODEL OF NEUROINFLAMMATION

Elena Lebedeva

A mathematical model of neuroinflammation is proposed that describes the interplay among the peripheral inflammatory response, microglial activation, neural tissue damage, changes in blood-brain barrier permeability, and the effects of preventive glucocorticoid administration. The model is formulated as a system of ordinary differential equations and is intended to investigate the conditions governing the transition from an acute inflammatory response to a stable chronic state. The analysis includes verification of well-posedness of the model, identification of equilibria, local stability analysis, bifurcation analysis, and parameter sensitivity analysis. Three dynamic regimes were identified: rapid resolution of inflammation, delayed recovery accompanied by persistent changes in the central nervous system, and transition to chronic neuroinflammation. The development of chronic neuroinflammation was shown to be associated with strengthening of the positive feedback circuit between central inflammatory mediators and activated microglia. The parameters exerting the greatest influence on the duration of the inflammatory response, accumulation of neural tissue damage, and decline in the effectiveness of glucocorticoid-mediated regulation were identified. The model may be used to interpret experimental data, assess the contributions of individual components of the inflammatory response, and investigate the conditions underlying the development of chronic neuroinflammation.

Bifurcation Analysis of Mathematical Model of HPV Transmission Between Individuals Influenced by Media Coverage

Putu Andika Bramastha

We consider a mathematical model of HPV transmission between individuals influenced by news media
coverage. The model is a four dimensional system of the first order of ordinary differential equations that
represent the interaction between individuals among population, i.e., susceptible, infected, recovered, and
cancer. In this paper, we propose the saturation function that represents the transmission rate of HPV influenced
by news media coverage. We focus our analysis on the existence and stability conditions of the equilibrium
points to determine the behavior of the system. Furthermore, by using bifurcation analysis, we found that the
system undergoes a forward bifurcation on a certain parameter.

Mathematical Modeling of Antimalarial Drug Resistance in Sub-Saharan Africa: Transmission Trajectories and Mitigation Strategies

Romain Glèlè Kakaï

Antimalarial drug resistance continues to threaten malaria control in Sub-Saharan Africa. While mathematical models of malaria transmission are well established, few have simultaneously accounted for asymptomatic reservoirs, treatment failure, and vector control within a drug-resistance framework and applied it comparatively across multiple high-burden countries. We developed a deterministic compartmental model that explicitly integrates asymptomatic and symptomatic infections, treatment pathways, treatment failure, and vector control to examine drug-resistant malaria transmission dynamics in Ghana, Burkina Faso, and Uganda from 2000 to 2023. Positivity, boundedness, and stability of the malaria-free equilibrium were established analytically. The basic reproduction number (R0) and control reproduction number (Rc) were derived using the next-generation matrix approach, and sensitivity analysis identified the main drivers of transmission, focusing on treatment failure. Model parameters were estimated using nonlinear least squares. Results revealed substantial
heterogeneity in transmission intensity across the three countries: Ghana and Burkina Faso exhibited lower transmission potential, while Uganda remained above the epidemic threshold throughout the study period. Treatment failure and asymptomatic infectivity emerged as the strongest drivers of sustained transmission. These findings highlight the need for context-specific intervention strategies that improve treatment effectiveness, target asymptomatic reservoirs, and strengthen vector control measures to reduce drug-resistant malaria transmission across the region.

A A Compartmental Model for Tuberculosis Transmission Dynamics with Control Measures

MORGAN WALICHO

Tuberculosis is a global endemic that claims millions of lives every year. Therefore,there is need for continuous research in order to understand its dynamics for effective prevention and control as recommended by WHO. The study developed a six compartmental $SVLATR$ mathematical model that incorporated TB transmission dynamics with control measures to assess their impact on TB spread . The threshold quantity called basic reproduction number $R_0$ ,that determines whether the disease persists and spreads or gets eliminated was computed using the Next Generation Matrix ($NGM$) and found to be $ R_0 \approx 1.73 > 1$ indicating persistence of the endemic. The model was used to predict future trends in TB and projected a decline in TB incidence,prevalence and mortality for the next 5 years but insufficient to fully eliminate TB. The stability properties of the system were analyzed using Jacobian matrix and eigenvalue analysis. The condition for stability of the Disease Free Equilibrium ($DFE$) is stable if $R_0 < 1$ . Since $R_0 > 1$ it was found to be unstable while Endemic Equilibrium ($EE$) is locally asymptotically stable since $R_0 >1$ . Bifurcation analysis indicated that the system is at the endemic state and measures to lower reproduction number below unity are needed to eliminate TB. The simulated results using the real world epidemiological data indicates persistence of TB under the current intervention measures. This modeling approach provides policymakers and public health stakeholders with evidence based recommendations for improving TB control.