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The present study was conducted to document the ethnomedicinal plants used against jaundice by the tea tribes of Morigaon district of Assam, India. An ethnomedicinal field study was carried out from June 2016 - July 2017. Information was gathered by using a semi-structured questionnaire about the traditional knowledge of medicinal plants used against jaundice by the tea tribes of Morigaon district of Assam. Documented data was evaluated using the quantitative ethno-botanical indices of fidelity level (FL), Use Value (UV) and Family Use Value (FUV). From the ethno-botanical investigation, a total of 39 species of plants covering 36 genera and 27 families respectively have been enumerated. A total of 53 informants aged from 20-75 years were interviewed to record the ethnomedicinal data. Lamiaceae was the dominant family. Among the plant portions, leaves were most frequently used. Among the 39 medicinal plant species recognized mostly were herbs. The plants species having the highest use value were Drymaria cordata trailed by Xylosma longifolia and Achyranthes aspera, Aegle marmelos, Alstonia scholaris and Justicia gendarussa . The fidelity level was 100% for Achyranthes aspera, Cheilocostus speciosus, Clerodendrum infortunatum, Justicia gendarussa, Lawsonia inermis, Coffea benghalensis and Saccharum officinarum . The tea tribes of Morigaon district still relies on herbal therapies for curing jaundice. Coffea benghalensis has not been previously reported as a remedy of jaundice from Northeast India. Further research is needed to investigate the phytochemistry and pharmacological effectiveness of the plant species that could be the basis for the isolation and development of some novel phyto-therapeutic active compounds in the future.

In the present paper we formulate a mathematical model of two predators living on a single biotic prey. The two predators interfere directly with each other. The predation function for the two predators are assumed to be different - one follows the mass action kinetics while the other obeys Holling type-II functional response. We also assume that one of the predators is economically viable and undergo harvesting at a rate proportional to its density. We perform local stability analysis about the boundary states where one of the predator species is absent. It is seen that, the existence and/or extinction criteria of each predator is controlled by the predation rates of one or both the predators. The interior equilibrium point exhibits unstable oscillatory behavior in the local analysis. We also perform a global analysis using Lyapunov function and LaSalle’s principle which shows global stability around this point for limited carrying capacity of prey. Finally we model the phenomenon of random harvesting by perturbing the harvest rate using Gaussian white noise. The resulting stochastic differential equation model is analyzed for exponential mean square stability which is shown to depend on the harvesting effort. Numerical simulation study of the model equations are also carried out.

Though bilinear and standard incident rates have been used frequently in classical epidemic models, nonlinearity in infection incidence is considered to be an useful modification due to its proximity with various realistic situations of disease propagation among ecological populations. In the present research, we consider an epidemiological model with SIS disease in the population. Infection is assumed to propagate following nonlinear incidence. First, we perform a stability and bifurcation analysis of the system around different equilibria from a local perspective. It is observed that the infected incidence fraction (p) plays the key role in controlling the disease dynamics. Then, using an iteration scheme and comparison argument, we investigate the global stability criteria of the model system around the endemic state and infer that the disease will persist among the species in the long run. Numerical simulation study is also carried out to illustrate and augment the analytical findings.

In the present paper, we consider a mathematical model of ecosystem population interaction where the population suffers from a susceptible-infectious-susceptible disease. Dispersal of both the susceptible and the infective is incorporated using reaction-diffusion equations. We first study the stability criteria of the basic (non-spatial) model around the disease-free and the infected steady states. We find that the loss rate of the infective species controls disease prevalence. Also without predation pressure, the disease will continue to exist among the population. Then we analyze the spatial model with species dispersal in constant as well as in time-varying form. It is observed that though constant dispersal is unable to generate diffusion-driven instability, dispersal with sinusoidal variation in dispersion rate can generate diffusive instability when the wave number of the perturbation lies within a given range. Numerical simulations are performed to illustrate analytical studies.

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.

In this paper, a food-chain model in a mangrove ecosystem with detritus recycling is analyzed. From the stability analysis of the delayed homogeneous system, an interval for the parameter representing detritus-detritivores interaction rate is obtained that imparts stability to the system around the coexistent state. Next, we have studied the model in a nonhomogeneous environment. The analysis revealed the existence of a subinterval of the above mentioned interval such that when the above interaction-rate lies within this interval, the system will undergo diffusion driven instability. Finally, we show the existence of travelling wave solutions for the said ecosystem. Numerical simulations are carried out to augment analytical results.

The present paper deals with the mathematical analysis of a prey–predator model where the prey population is assumed to live in two distinct habitats and the predator consumes prey from both these habitats with a switching tendency. The dynamical behavior of the system is investigated from the point of view of stability and bifurcation aspects. It has been found that the mortality rate of the predator plays an important role in controlling the system dynamics. Finally, a detailed study of the Hopf-bifurcating solutions is carried out and the criteria for subcritical and supercritical Hopf-bifurcation derived. Numerical simulations are performed in support of analytical results.

A mathematical model consisting two harmful phytoplankton and zooplankton with discrete time lags in the mortality of zooplankton due to liberation of toxic substances by harmful phytoplankton has been considered. A stable co-existence of all the species has been observed for no-delay situation. Introduction of single delay in the system cause recurrent algal bloom and a threshold for the delay parameter has been estimated. Further, presence of multiple (two) delays control the oscillatory situation and can be used for termination of planktonic bloom. The analytical results as well as numerical simulations of our study lead to several threshold values for the delay parameters which play important roles in the marine ecological problems. An interesting observation is that multiple delay resolves plankton ‘paradox’ and establish a positive effect of competitive exclusion principle for stable co-existence of the species.

The present paper deals with the wave train solutions of a generalized reaction-diffusion system. A comparative study of the nature of waves of the system in the presence of both self-diffusion and cross-diffusion has been performed. A two-species oscillatory model has also been considered as an example and analysed for its spiral wave solutions.

A mathematical model describing the biochemical interactions of the luteinizing hormone (LH), luteinizing hormone–releasing hormone (LHRH), and testosterone (T) is presented. The model structure consists of a negative feedback mechanism with transportation and secretion delays of different hormones. A comparison of stability and bifurcation analysis in the presence and absence of delays has been performed. Mathematical implications of castration and testosterone infusion are also studied. 2000 Mathematics Subject Classification: 37G15.

An ecological model for prey-predator planktonic species has been considered, in which the growth of prey has been assumed to follow a Holling type II function. The model consists of two reaction-diffusion equations and we extend it to time-varying diffusivity for plankton population. A comparative study of local stability in case of constant diffusivity and time varying diffusivity has been performed. It has been found that the system would be more stable with time varying diffusivity depending upon the values of system parameter.