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Dynamics of an autonomous food chain model and existence of global attractor of the associated non-autonomous system

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International Journal of Biomathematics 2019年第8期12卷 1-31页

作者： jyotirmoy roy Shariful Alam Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur B.GardenHowrah-711103India

In this paper,we have analyzed a tri-trophic food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.

关键词： Food chain model DVM Hopf bifurcation limit cycle periodic solution global attractor

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Towards Developing Communication Strategies for HIV/AIDS Control among the Scheduled Tribes and Scheduled Castes Women in Three Northeastern States of India

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World Journal of AIDS 2013年第4期3卷 367-377页

作者： Kalyan B. Saha Damodar Sahu Uma C. Saha Ravendra K. Sharma M. Muniyandi Prabhaker Mishra Chhanda Mallick jyotirmoy roy Amal K. Bhunia Samiran Bisai Arvind Pandey Department of Anthropology Vidyasagar University Midnapore India Department of Biomedical Laboratory Science & Management Vidyasagar University Midnapore India Department of Community Medicine M. M. Institute of Medical Sciences and Research Ambala India National Institute of Medical Statistics (ICMR) New Delhi India Regional Medical Research Centre for Tribals (ICMR) Jabalpur India Xavier Institute of Development Action & Studies (XIDAS) Jabalpur India

HIV/AIDS spread has opened a Pandora of medical and health problems apart from creating serious socio-psychological trauma for the victims and their families. Despite the governmental effort to curve the growing infection, very little success has been achieved. The northeastern region of India presents a very peculiar situation due to recurrent insurgency in all its states for long time and thus it became instrumental in paralyzing the social and health machineries to an extent, which still deteriorated the futile national effort to check the deadly infection. The study tried to understand the level of awareness and correct knowledge among the underprivileged scheduled tribes and scheduled castes women in the age group 15 -44 by exploring data from district level of Rapid Household Reproductive and Child Health Project Phase I (1998) and Phase II (1999) for Assam, Manipur and Nagaland and suggested a strategy to control the infection in the region. It is found that HIV/AIDS awareness was 59% among the women in all the three states with very few among them who had correct understanding of its prevention. A pronounced difference in the level of awareness was observed with respect to age, economy and residential status of the respondents.

关键词： AIDS Awareness Transmission Prevention & Misconception Communication Strategy

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