J Pal

Paradox of enrichment: A fractional differential approach with memory

n Abstractn n The paradox of enrichment (PoE) proposed by Rosenzweig [M. Rosenzweig, The paradox of enrichment, Science 171 (1971) 385–387] is still a fundamental problem in ecology. Most of the solutions have been proposed at an individual species level of organization and solutions at community level are lacking. Knowledge of how learning and memory modify behavioral responses to species is a key factor in making a crucial link between species and community levels. PoE resolution via these two organizational levels can be interpreted as a microscopic- and macroscopic-level solution. Fractional derivatives provide an excellent tool for describing this memory and the hereditary properties of various materials and processes. The derivatives can be physically interpreted via two time scales that are considered simultaneously: the ideal, equably flowing homogeneous local time, and the cosmic (inhomogeneous) non-local time. Several mechanisms and theories have been proposed to resolve the PoE problem, but a universally accepted theory is still lacking because most studies have focused on local effects and ignored non-local effects, which capture memory. Here we formulate the fractional counterpart of the Rosenzweig model and analyze the stability behavior of a system. We conclude that there is a threshold for the memory effect parameter beyond which the Rosenzweig model is stable and may be used as a potential agent to resolve PoE from a new perspective via fractional differential equations.n n

The Impact of Vaccination to Control Human Papillomavirus Dynamics

Human papillomavirus (HPV) has been a prevalent virus for a long time. The number of cancer cases from benign tumours is constantly increasing and HPV is playing an important role, more aggressively is evolving as cervical cancer in young females. More than 170 types of HPV virus exists and among them some are “High-risk” variety, some are “Low-risk” variety. The control of this virus outbreak remains a challenge till date. The aim of this study is to investigate the role of vaccination as a control strategy in decreasing of the spread of the disease. In this research article, we formulated a model considering high-risk-type HPV, low-risk-type HPV, and low–high risk (infected by both low-risk and high-risk)-type HPV. We derive the basic reproduction ratio and also show that there exists a disease-free equilibrium, which is locally asymptotically stable. Furthermore, an analysis is then performed on crucial parameters in order to determine their importance and potential impact on HPV dynamics. Our analytical and numerical analysis reveals that HPV infection can be reduced by using vaccination as a control strategy.

The generalization of an n-patch model for Leishmaniasis

Leishmaniasis is a vector borne disease, which is caused by a protozoan parasite. Infected female sandflies textit{(Phlebotomine sp.)} are responsible for such disease transmission. People can carry some species of Leishmania for long periods and the incubation period for Leishmaniasis may be few weeks or several months. Migration depends on host immunological status also. Leishmaniasis is endemic globally in ninety eight countries. Spread of the disease is intensely dependent on migration of the disease among human and vector between various regions or countries. Here, we formulate an

Effect of austempering treatment on microstructure and mechanical properties of high-Si steel

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How Memory Regulates Drug Resistant Pathogenic Bacteria? A Mathematical Study

-patch mathematical model (such patches can be some states, regions or countries) considering each patch have susceptible, infected human as well as susceptible and infected vector population. We have derived basic reproduction ratio for each patch as well as the general basic reproduction ratio for the system and shown that there exists a disease-free equilibrium that is locally asymptotically stable. Further, we study the system analytically and numerically when the migration between each patch of individual class of humans and vector effects the spreading of the disease. We also established the results taking into account for different number of patches for

Effect of enrichment on plankton dynamics where phytoplankton can be infected from free viruses

n=2

Role of macrophage in the disease dynamics of cutaneous Leishmaniasis: a delay induced mathematical study

. Our result reveals that the movement of human and vector from each patch to another patch plays an important role for spreading of the disease. https://doi.org/10.28919/cmbn/3361