Communication in Biomathematical Sciences

A Discrete Fractional-Order Predator-Prey Model with Cannibalism and Refuge: Implementation of Piecewise Constant Argument (PWCA) Method

2024-09-30T21:16:54+07:00

In this paper, we apply a Piecewise Constant Argument (PWCA) method to a fractional-order predator-prey model that incorporates predator cannibalism and prey refuge. The resulting discrete system is then analyzed dynamically, meaning we determine the equilibrium points and their stability. There are four equilibrium points: the origin, prey extinction, predator extinction, and coexistence. We find that the stability properties of these equilibrium points are more complex than those found in the continuous model. Additionally, we observe that the order of the derivative also influences the stability of these equilibrium points. These findings are confirmed through numerical simulations.

Age-structured SILV epidemic model on HPV and cellular dynamics with implicit impact of vaccination

2024-09-23T02:28:25+07:00

The implicit impact of vaccination on susceptible cells (epithelial layer) is studied on the basis of stability
analysis of dynamics of age-structured epidemic model of susceptible cells, infected cells and cells of lesion
tissue (dysplasia and cancer), human papillomavirus (HPV). The efficacy of the vaccine indirectly influences the
HPV infection rate, budding number of HPV virions produced by a single infect-ed host cell (HPV replication),
and HPV death rate, thereby determining the types of dynamical regime of the cell-HPV population. The model
possesses unique disease-free and unique endemic equilibria (DFE and EE, respectively). Asymptotically stable
DFE is associated with the resilience of the epithelial layer to HPV infection. The analysis of the model reveals
independent factors affecting the stability/instability of DFE and EE: (i) cell death rate and proliferation rate,
(ii) vaccine efficacy (HPV infection rate, bud-ding number of HPV virions, apoptosis rate of infected cells and
HPV death rate), and (iii) DFE value of epithelial tissue size. The latter factor plays a role of environmental
capacity of HPV, depends on the initial size of the epithelial layer and affects the stability of DFE. Numerical
experiments illustrate the theoretical results obtained in the paper.

STUDY THE SPREAD OF CORONAVIRUS IN KERALA USING MAPPER ALGORITHM

2024-09-22T02:00:19+07:00

In this paper we apply Mapper algorithm to visualize the spread of coronavirus in Kerala during the first and the second wave. The topological features help to compare the data according to various parameters like time, population etc. We collected data regarding number of corona cases reported in the state. Using Mapper algorithm, we produced Mapper graph of five-dimensional data with co-ordinates latitude, longitude, population density, number of corona cases reported and time. Thereafter applied Mapper algorithm to the data by removing certain co-ordinates. Comparing these figures, we can see that geography has not much role in the spread of corona virus. But population density of districts affects the spread at some extend.

Optimal Management of Nitrogen Pollution

2024-09-10T22:54:15+07:00

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.