Communication in Biomathematical Sciences

Transmission Dynamics and Cost-Effective Control Studies of Drug-Sensitive and Drug-Resistant Tuberculosis

Krishna Kiran Vamsi Dasu

Tuberculosis (TB) is a highly infectious airborne disease responsible for millions of deaths globally each year. Mycobacterium tuberculosis exists in both drug-sensitive (DS) and drug-resistant (DR) forms posing significant challenges to treatment and control. In this work, we studied a non linear transmission
model for drug-sensitive and drug-resistant TB and analyzed its dynamics considering vaccination along with the standard drug regimen as recommended by National Tuberculosis Elimination Programme (NTEP) as a control measure to reduce disease transmission. We also studied the effect of BCG vaccination
alone on the disease burden and found that it significantly reduces susceptibility and leads to a substantial decrease in the number of infected individuals. Unknown parameters in the model are estimated using the least squares method. Numerical simulations show that the disease-free equilibrium
is stable if max(R0s,R0r) < 1. The stability of mono-existent and co-existent equilibria are analytically demonstrated via Lyapunov function methods. We also show that loss to follow-up and treatment failure rates in driving drug resistance significantly increases the TB-related mortality. An optimal control
model is developed to evaluate the effectiveness of different intervention strategies incorporating separate control measures for DS-TB and DR-TB in line with NTEP recommendations. Our analysis highlights the significant role of the BCG vaccination along with NTEP recommended drug regimens in minimizing
the disease burden. A cost-effectiveness analysis using the ICER method is conducted to identify the most cost-effective control measure. This study offers valuable insights into TB control strategies and their cost-effectiveness while emphasizing the critical role of treatment adherence and success in reducing
the prevalence of drug-resistant cases.

Dear Editorial Team of the Communication in Biomathematical Sciences Journal, I hereby represent the co-authors in submitting a literature review manuscript entitled "Application of Mathematical Models in Population Studies and Conservation of Birds of P

Edoward Raunsay

Mathematical modeling plays a crucial role in understanding wildlife population dynamics and supporting evidence-based conservation policies. However, quantitative approaches are still relatively limited in population studies of birds of paradise (Paradisaeidae), particularly in eastern Indonesia. This study aims to develop and apply a modified logistic growth model to represent the population dynamics of birds of paradise in Papua. Specifically, this study aims to determine the most appropriate mathematical model, estimate intrinsic growth rates and environmental carrying capacity based on empirical parameters, and evaluate conservation scenarios through numerical simulations. The model integrates growth rate, natural mortality, hunting pressure, and environmental carrying capacity. Parameter estimation was performed using a nonlinear least squares method based on actual population data, while thirty-year projection simulations were performed using the Fourth-Order Runge–Kutta numerical method. The results show that the modified logistic model accurately represents population dynamics with a high level of model fit. Sensitivity analysis identified that intrinsic growth rates and environmental carrying capacity were the most influential parameters affecting long-term stability. Scenario simulations indicated that habitat restoration had the most significant impact on population recovery compared to reduced hunting. This research contributes theoretically to the integration of quantitative ecological models with conservation planning, and practically provides a scientific basis for adaptive conservation management.

A Seven-Dimensional Optimal Control Model for Respiratory Virus Infection

Ranu Paul

Respiratory viruses including influenza, RSV, HIV, and SARS-CoV-2—continue to pose major global health challenges, making it essential to understand how infections progress within the host and how treatments can be optimized. In this study, we develop a comprehensive within-host mathematical model that captures the interactions among wild-type and drug-resistant viral strains, immune response, antiviral therapy, cytokine-mediated inflammation, host health, and microbiome balance. We analyze the model to determine equilibrium points and derive expressions for both the basic reproduction number and the effective reproduction number under antiviral pressure. Sensitivity analysis identifies the most influential biological parameters driving infection outcomes. To explore optimal treatment strategies, we apply Pontryagin’s Maximum Principle and design time-dependent antiviral and immune-modulating controls. Our results provide insight into how combined therapeutic interventions can suppress viral replication, reduce inflammation, and preserve host health, offering a useful framework for designing more effective treatment strategies against respiratory viral infections.

Nonlinear host -vector model taking into account Vector aggregation and host preference

IDO Michel

We propose a mathematical model for the transmission of Tomato Yellow Leaf Curl Virus (TYLCV)

that incorporates vector aggregation of Bemisia tabaci and nonlinear incidence. We analyze the stability of

the disease-free and endemic equilibria using the basic reproduction number R0. Sensitivity analysis and

numerical simulations illustrate the influence of vector aggregation on the spread of the disease.