Communication in Biomathematical Sciences

Mathematical model of dengue transmission dynamics with adaptive human behavior

Jonecis Dayap, Jomar Rabajante

Dengue fever, a viral disease spread by {\it Aedes} mosquitoes, is a significant public health issue in tropical and subtropical regions. Behavioral adaptations in response to perceived infection risks can significantly reduce disease incidence and prevalence through the adoption of control measures. However, most existing models developed to assess the mitigation of dengue only implicitly account for this adaptive behavior within the dynamics of disease transmission. In this paper, we propose a mathematical model that explicitly incorporates adaptive human behavior in response to community infection levels into the transmission dynamics of dengue and investigates how this behavior affects transmission. Analytical results of the model reveal that the disease-free equlibrium is locally asymptotically stable when the control reproduction number ($\mathcal{R}_c$) is less than 1. The model parameters are calibrated using daily dengue case data from the 2015 outbreak in Kaohsiung City, Taiwan, resulting in a calculated reproduction number ($\mathcal{R}_c$) of 1.42. Sensitivity analysis indicates that to reduce the reproduction number, efforts should focus on reducing mosquito-human contact, controlling the mosquito population, and improving hospital treatment. Numerical simulations demonstrate that positive behavioral changes in response to increasing infection levels significantly reduce dengue cases when self-protective and vector control measures are effectively implemented. Our results emphasize the importance of enhancing these behavioral changes to achieve a substantial reduction in dengue incidence. This highlights the critical role of reporting disease prevalence, educating individuals on effective dengue mitigation strategies, and ensuring access to resources necessary for high-efficacy self-protection and vector control measures. By promoting awareness and providing support for control measures such as mosquito repellents, bed nets, insecticide-treated curtains, and community clean-up drives to eliminate mosquito breeding sites, governments can significantly enhance the effectiveness of dengue control programs.

Study the impact of Delay in Deform Biological Population with Stability and Optimal Control due to Externally Emitted Toxicant

Digvijai Singh, Joydip Dhar, Alok Kumar Agrawal

Nowadays, the environment's surroundings are pressing issues, and for ecological concerns, the toxicant's effects 
are crucial and significant issues mathematically and experimentally. Each Biological population has its structure and functioning, but due to these toxicants last few years, there have been rapidly abnormal 
changes in their function like productivity, change in shape, necrosis, etc. Most of the time, ecologist focused 
on their research on the existence or extinction of biological species. Information is also supporting their 
theories. However, there is less information regarding abnormal changes in their behavior and functioning. The 
present study proposes an Eco-toxicological model for biological population species which is affected and losing 
their identity in the form of deformity with a delay period. We investigate an autonomous four-compartmental 
system with its dynamical behavior, which is affected by toxic substances emitted by some external source.

Further boundedness and local stability have been studied. The analytical results show that the system's 
stability is disturbed as the deformation delay increases. After a critical delay value, the system exhibits 
bifurcation,i.e., population density oscillates over time. The optimal control model is approached to build 
Hamiltonian function to minimize their cost. Finally, numerical authentication carries the consistency of 
analytic results with the theoretical approach.

Geometric Analysis of Agarwood Inoculation Model

Mamika Ujianita Romdhini

Decomposed wood with aromatic resins is called agarwood. It is created biotically by bacterial, fungal, and physical infections from wounds like fires, lightning strikes, insect and mammal attacks, and broken branches. The formation of natural agarwood has encouraged the development of artificially induced agarwood. This study aims to develop a mathematical analysis of the agarwood inoculation model where the inoculation hole pattern is made in a spiral. The method used is a geometric analysis and Pythagoras theorem. The results show the formula of the number of inoculation holes based on the tree's diameter. In addition, the length of the stem to produce one kilogram of agarwood is provided.

A Simpler model equivalent to SIR model with time-explicit solution

Ramachandran Mankali

This note proposes a simpler mathematical model equivalent to the SIR epidemic model. The proposed model reduces to a first-order differential equation and has an advantage in obtaining a stable and time-explicit solution for the infection. Then, using certain transmission and recovery time-varying functions, using inputs estimated from actual data, we deduce the analytical expression for the epidemic curve. The expressions are shown to be the Gaussian and Gumbel distributions. These distributions have been widely used to fit the actual Covid-19 data seen in many countries. The epidemic is analysed using illustrations and showcases a similarity with the Covid-19 curves seen in India.