Ingested metallic foreign body lodged in the appendix.

An 8-year-old child ingested a metallic screw 3 months prior to admission. At laparotomy, the foreign body was found to be lodged inside the vermiform appendix, and was removed by appendicectomy.

Impacts of incubation delay on the dynamics of an eco-epidemiological system--a theoretical study.

Parasite and predator play significant role in trophic interaction, productivity and stability of an ecosystem. In this paper, we have studied a host-parasite-predator interaction that incorporates incubation delay. How the qualitative and quantitative behaviors of the system alter with the incubation delay have been discussed both from mathematical and biological point of views. It is observed that for a lower infection rate, the system is stable for all delays; but for a higher infection rate, there exists a threshold value of the delay above which the system is unstable and below which the system is stable leading to the persistence of all the species. Also, the instability arising from the incubation delay may be controlled if somehow the growth rate of predator population is increased. Numerical studies have also been performed to illustrate different analytical findings.

A mathematical model on the effect of M. denticulata weed on different winter crops.

Many weeds interfere with the productivity of wheat and other winter annual crops; however, one common weed Medicago denticulata, appears to have a beneficial effect. An experiment was conducted at Agricultural Experimental Farm of the Indian Statistical Institute, Giridih, Jharkhand to observe the effect of M. denticulata (a legume) on different crops yield of barley (Hordeum vulgare Sensu lato), linseed (Linum usitatissimum L.), Indian mustard [Brassica juncea (L.) Czernj. & Cosson] and wheat (Triticum aestivum L.). The commensalisms interaction was studied, in which one species benefits, while the other is unaffected, between the crops, M. denticulata and other weeds, to observe the role of medicago as biological control agent of other weeds for enhancement of crop productivity. Further, a statistical test was performed to establish the effect of M. denticulata and weed infestations based on one-step Markov structure of the covariance matrix of the biomass. This permitted development of a mathematical model of a crop-M. denticulata-other weeds system and their interactions through direct and indirect competition for resources. Crops yield decreased considerably due to the presence of other weeds, while it increased due to introduction of medicago and hence medicago acted as a controlling agent in a crop-M. denticulata-other weeds system. Our mathematical analysis supported the experimental findings. The model parameters are estimated through a nonlinear least square and stochastic differential equations. Moreover, some thresholds for the growth of medicago population came out from our analysis that may be used as a biological control threshold for the enhancement of crop productivity.

Role of two toxin-producing plankton and their effect on phytoplankton-zooplankton system--a mathematical study supported by experimental findings.

Plankton is the basis of the entire aquatic food chain. Phytoplankton, in particular, occupies the first trophic level. Plankton performs services for the Earth: it serves as food for marine life, gives off oxygen and also absorbs half of the carbon dioxide from the Earth's atmosphere. The dynamics of a rapid (or massive) increase or decrease of plankton populations is an important subject in marine plankton ecology and generally termed as a 'bloom'. Harmful algal blooms (HABs) have adverse effects on human health, fishery, tourism, and the environment. In recent years, considerable scientific attention has been given to HABs. Toxic substances released by harmful plankton play an important role in this context. In this paper, a mathematical model consisting of two harmful phytoplankton and zooplankton system will be discussed. The analytical findings will be verified through our experimental observations which were carried out on the eastern part of Bay of Bengal for the last three years.

Occurrence of planktonic blooms under environmental fluctuations and its possible control mechanism--mathematical models and experimental observations.

Planktonic blooms and its control is an intriguing problem in ecology. To investigate the oscillatory successions of blooms, three simple phytoplankton-zooplankton systems are proposed. It is observed that if the uptake function is linear and the process of toxin liberation is instantaneous, the oscillatory nature of blooms is not observed. On the other hand, periodic planktonic blooms are observed when toxin liberation process follows discrete time variation. The bloom phenomena described by this mechanism can be controlled through toxin producing phytoplankton (TPP). Introducing environmental fluctuation in the system, a critical value of time delay in terms of correlation time of the fluctuation is worked out. We observed from our mathematical analysis, numerical simulation and field observation that TPP and control of the rapidity of environmental fluctuation are key factors for the termination of planktonic blooms.

Dynamics of nutrient-phytoplankton interaction in the presence of viral infection.

The present paper deals with the problem of a nutrient-phytoplankton (N-P) populations where phytoplankton population is divided into two groups, namely susceptible phytoplankton and infected phytoplankton. Conditions for coexistence or extinction of populations are derived taking into account general nutrient uptake functions and Holling type-II functional response as an example. It is observed that the three component systems persist when the infected phytoplankton population is not able to consume nutrient.

Toxin-producing plankton may act as a biological control for planktonic blooms--field study and mathematical modelling.

Termination of planktonic blooms is of great importance to human health, ecosystem, environment, tourism and fisheries. Toxic substances released by plankton play an important role in this context. The effect of toxin-producing plankton (TPP) on zooplankton is observed from the field-collected samples and mathematical modelling. Information from both the studies led us to suggest that TPP may terminate the planktonic blooms by decreasing the grazing pressure of zooplankton and thus acts as a biological control.

A delay differential equation model on harmful algal blooms in the presence of toxic substances.

The periodic nature of blooms is the main characteristic in marine plankton ecology. Release of toxic substances by phytoplankton species or toxic phytoplankton reduce the growth of zooplankton by decreasing grazing pressure and have an important role in planktonic blooms. A simple mathematical model of phytoplankton-zooplankton systems with such characteristics is proposed and analysed. As the process of liberation of toxic substances by phytoplankton species is still not clear, we try to describe a suitable mechanism to explain the cyclic nature of bloom dynamics by using different forms of toxin liberation process. To substantiate our analytical findings numerical simulations are performed and these adequately resemble the results obtained in our field study.