On stochastic differential equations and equilibrium distribution: a conditional moment approach

In the recent past there have been several attempts to obtain the equilibrium distribution of multiple populations and their moments in the context of some biological or ecological processes (e.g., Matis and Kiffe in Biometrics 52:155, 1996; Matis and Kiffe in Environ Ecol Stat 9:237, 2002; Renshaw in J Math Appl Med Biol, 15:1, 1998). In particular, the method of cumulant truncation (Matis and Kiffe in Biometrics 52:155, 1996) is a pioneering work in this field. However it requires solving a large number of cumulant functions even in the case of two simultaneous differential equations. Besides the solutions are approximate and depend on the precision of the software. Renshaw (Math Biosci 168:57, 2000) provided a nice extension of the univariate truncated saddle point procedure to multivariate scenarios. But this approach involves a multivariate Newton-Raphson type iterative algorithm whose performance and convergence are critically dependent on the choice of the initial values. In the present paper we propose a new and simple approach to obtain the equilibrium distribution of populations and their conditional moments in a system of differential equations of any dimension. Our proposed method, which is a natural extension of the classical variational matrix approach, has several advantages which are discussed in detail in the paper; among other things it includes the derivation of additional conditions which can be interpreted as environmental surrogates.     

Role of standard incidence in an eco-epidemiological system: A mathematical study

Ecology and epidemiology are two major fields of study in their own right, but they have some common features. [Chattopadhyay, J., Pal, S., El Abdllaoui, A., 2003. Classical predator–prey system with infection of prey population—a mathematical model. Math. Meth. Appl. Sci. 26, 1211–1222] considered a predator–prey model with disease in the prey population. They analyzed the system based on the assumption that horizontal incidence follows simple mass action incidence. Mass action incidence is appropriate for a constant population, but for a large population, standard incidence is more appropriate. The complicated dynamics around (0, 0, 0) arise because of standard incidence. The conditions under which the population reaches the origin either by following the axis or in a spiral pattern were determined. Numerical experiments were performed to observe the dynamics of the system with mass action incidence and standard incidence. This investigation showed that the infection rate plays a crucial role for predicting the behavior of the dynamics in the long run.     

Evaluation of hematological changes in population exposed to fluoride

Absorption of fluorine compounds produces chronic toxicity and the hematological changes appear earlier in blood than other organs. A study was undertaken to determine the status of hematological changes in the individual residing in fluoride-contaminated area. Two hundred and fifty nine and 233 subjects from the contaminated area and an unaffected area, respectively, were selected for hematological investigations. Total erythrocytes (red blood corpuscles (RBC)), total leucocytes (white blood corpuscles (WBC)), and hemoglobin (Hb) concentrations were determined in these populations. Results revealed that Hb values were significantly lower among all age groups in the exposed population compared to control subjects. There was a quantitative rise in WBC counts in study subjects compared to controls. The RBC counts showed reduction among exposed population.     

Water quality of the River Ganga (The Ganges) and some of its physico-chemical properties

Summary The water qualities of the River Ganga (The Ganges) over a short stretch from Swarupganj to Barrackpore (in West Bengal) have been determined and are compared with the values reported by the National Environmental Engineering Research Institute of India for the periods 1972–74 and 1979–80. The water quality is generally bad, but not at such alarming levels as previously determined by other agencies. Biochemical and chemical oxygen demand (BOD and COD) levels are high but within tolerable limits. Dissolved oxygen (DO) levels are are fairly high, indicating a reasonable self-purifying capability for the River Ganga. However, nutrient loads containing N and P have increased enormously in recent years.     

Critical analysis of turbulence models for simulating positive surge waves in open channels in a RANS-VOF setup

Environmental Fluid Mechanics - The study presents a systematic assessment of 2D RANS-VOF simulation of positive surge wave propagation in open channels using three widely used turbulence models:...