Publications

This study presents a novel two-strain nonlinear mathematical model to assess the impact of treatment availability and adherence, on the spread of human immunodeficiency virus (HIV) in a community. First, we establish the well-posedness of the proposed model in an epidemiological context. The basic reproduction number for both the strains is determined by the next-generation matrix approach. The local and global analysis of existent equilibrium points using stability and bifurcation theory suggests that the drug-sensitive infected population faces competitive exclusion at lower relative transmission rates of this strain. For higher relative transmission rates of the infection, both infected populations coexist for a long time. The system exhibits transcritical bifurcation and Hopf bifurcation at multiple points with respect to various model parameters. Finally, we validate all the analytical results with an extensive numerical analysis using MATLAB R2023b. In summary, this study provides various conditions for applying different strategies to control the overall disease burden from the system.

We describe a deterministic and a stochastic model to understand the dynamics of chronic myelogenous leukemia (CML). The deterministic model comprises the interaction between leukemic cells at their different stages in CML and the autologous immune response. For this, we consider a system of ordinary differential equations, estimate its parameters and present the stability analysis for the existing equilibrium points. The results obtained are illustrated through appropriate numerical simulations. In case of the stochastic model, we consider only two cellular populations of stem cells and obtain the probability-generating functions for both these cells, both of which are visualized for illustrative cases. Our results show that a lower growth rate of cycling leukemic stem cells or a higher recruitment rate of immune cells which represents a suitable profile for suppressing the effect of CML on the patient.

A two-strain model, comprising of drug-sensitive and drug-resistant strains, is proposed for the dynamics of Human Immunodeficiency Virus (HIV) spread in a community. A treatment model is introduced by taking drug adherence into account. The treatment-free model is analyzed for the effect of treatment availability and drug adherence on disease dynamics. The analysis revealed that for the treatment-free model, at least one strain faces competitive exclusion, and co-existence of both strains is not possible. On the contrary, both strains may co-exist in presence of treatment. The analysis carried out was both local, as well as global. A comprehensive bifurcation analysis showed periodic behaviour and all solutions approached a stable limit cycle for a wide range of parametric values. Overall, we concluded that the treatment availability and drug adherence play a significant role in determining the dynamics of HIV spread. Numerical simulations are performed to validate the analytical results using MATLAB.

A natural food web system involves a diverse community of natural enemies and one of the widespread and common phenomena of such systems is intraguild predation (IGP) (i.e., presence of eating and killing among potential competitors). Here, we investigate the dynamics of a food web system with Allee effect and intraguild predation. In the present study, generalist and specialist natural enemies competing for a shared resource (prey) (intraguild predation) have been introduced. The Allee effect has also been incorporated in the shared prey growth rate. We investigate how parameters defining Allee effect and intraguild predation affect the long-term persistence, extinction and co-existence regions of such species. We outline the conditions under which different types of interior and non-interior equilibria exist and are locally stable. Bi-stable dynamics has also been investigated for the proposed model system for a suitable range of parametric values. A threshold condition on the strength of Allee effect has been obtained assuring the absence of IG predator population along with extinction region of shared prey. To understand the dynamics of the system, a comprehensive study of bifurcation analysis has also been provided taking Allee effect and fertility rate of intraguild predator as bifurcation parameters. These two parameters generate various interesting bifurcations like saddle-node bifurcation and Hopf-bifurcation. We have obtained different parametric regions of Allee parameter for the existence of different boundary and interior equilibria. All the analytical results related with local stability of equilibrium points and all possible successive bifurcations have been supported by different numerical examples, one and two parameter bifurcation diagrams, bi-stability diagram and stability regions of all possible equilibrium points. The impacts of Allee effect on co-existence, stability, extinction of species, their persistence, bistability and bifurcations have been explicitly discussed and the whole dynamics has also been successfully compared with the dynamics of food web without Allee effect. It is observed that the introduction of Allee effect and IG predator induce more rich dynamics and compel the system to be more sensitive to initial population densities.

A central challenge in Human Immunodeficiency Virus (HIV) public health policy lies in determining whether to universally expand treatment access, despite the risk of sub-optimal adherence and consequent drug resistance, or to adopt a more strategic allocation of resources that balances treatment coverage with adherence support. This dilemma is further complicated by the need for timely switching to second-line therapy, which is critical for managing treatment failure but imposes additional burdens on limited healthcare resources. In this study, we develop and analyze a compartmental model of HIV transmission that incorporates both drug-sensitive and drug-resistant strains, diagnosis status, and treatment progression, including switching to second-line therapy upon detection of resistance. Basic reproduction numbers for both strains are derived, and equilibrium analysis reveals the existence of a disease-free state and two endemic states, where the drug-sensitive strain may be eliminated while the drug-resistant strain persists. Local and global sensitivity analyses are performed, using partial rank correlation coefficient (PRCC) and Sobol methods, to identify key parameters influencing different model outcomes. We extend the model using optimal control theory to assess multiple intervention strategies targeting diagnosis, treatment initiation, and adherence. A novel dynamic control framework is proposed to achieve the UNAIDS 95-95-95 targets through efficient resource allocation. Numerical simulations validate the analytical results and compare the effectiveness and cost-efficiency of control strategies. Our findings highlight that long-term HIV epidemic control depends critically on prioritizing adherence-focused interventions alongside efforts to expand first-line treatment coverage.

In this study, we propose and analyze a two-dimensional prey-predator model with the harvesting of both prey and predator. The species are harvested according to the catch-per-unit effort (CPUE) hypothesis. It is assumed that the predator is partially dependent upon the prey population and followed by Holling type-III functional response. Steady states of the system are obtained, and local and global stability analysis is performed to examine the long-term behavior of the system. We also examine the effect of harvesting on the dynamics of the system. It is noticed that for higher values of harvesting efforts, the prey population becomes extinct via a transcritical bifurcation. We derive an optimal harvesting policy and obtain the optimal steady state solution and optimal harvesting efforts using Pontryagin’s Maximum Principle. Lastly, some numerical illustrations are presented in support of our theoretical findings. For a chosen set of parameters, we obtain the threshold value of some parameters beyond which the harvesting of prey biomass must be stopped for the sustainable growth of the species.