J.B. Shukla

Modeling and analysis of effects of awareness programs by media on the spread of infectious diseases

In this paper, a non-linear mathematical model for the effects of awareness programs on the spread of infectious diseases such as flu has been proposed and analyzed. In the modeling process it is assumed that disease spreads due to the contact between susceptibles and infectives only. The growth rate of awareness programs impacting the population is assumed to be proportional to the number of infective individuals. It is further assumed that due to the effect of media, susceptible individuals form a separate class and avoid contact with the infectives. The model is analyzed by using stability theory of differential equations. The model analysis shows that the spread of an infectious disease can be controlled by using awareness programs but the disease remains endemic due to immigration. The simulation analysis of the model confirms the analytical results.

Modeling and analysis of the algal bloom in a lake caused by discharge of nutrients

In this paper, a nonlinear model for the algal bloom in a lake caused by excessive flow of nutrients from domestic drainage and water runoff from agricultural fields, is proposed and analyzed. This model considers interactions of cumulative concentration of nutrients, density of algal population, density of detritus and concentration of dissolved oxygen in the lake. It is assumed that detritus, which is formed due to death of algae, supplements the cumulative concentration of the nutrients in the water body, using dissolved oxygen in the process. It is shown that the equilibrium level of algal population is highly dependent on the cumulative rate of discharge of inputs of nutrients in the lake and as this cumulative discharge increases the equilibrium level of algal population increases leading to eutrophication. It is also shown that the equilibrium level of dissolved oxygen decreases but that of detritus increases, as the rate of input of cumulative discharge increases. The same results are also found by numerical solution of the model.

Modelling the spread of carrier-dependent infectious diseases with environmental effect

Many infectious diseases spread by carriers such as flies, ticks, mites, snails, etc. In this paper an SIS model for carrier-dependent infectious diseases, like cholera, diarrhea, etc. caused by direct contact of susceptibles with infectives as well as by carriers is proposed and analyzed assuming the growth of both the human and the carrier populations logistic. It is assumed further that the density of carrier population increases with the increase in the cumulative density of discharges by the human population into the environment. The mathematical model is analyzed for the following two cases: (i) the rate of cumulative environmental discharges Q is a constant, and (ii) the rate of cumulative environmental discharges Q is a function of the population density. This model is analyzed using usual theory of differential equations and computer simulation. By computer simulation it is concluded that if the growth of carrier population caused by conducive household discharges increases, the spread of the infectious disease increases.

MODELLING AND ANALYSIS OF THE SPREAD OF MALARIA: ENVIRONMENTAL AND ECOLOGICAL EFFECTS

In this paper, general SIS and SIRS models with immigration of human population for the spread of malaria are proposed and analyzed. Effects of natural as well as human population density related environmental and ecological factors, which are conductive to the survival and growth of mosquito population, are considered. It is shown in both the cases that as the parameters governing environmental and ecological factors increase, the spread of malaria increases. It is also found that due to immigration, this infectious disease becomes more endemic.

Modeling and Analysis of the Spread of Carrier Dependent Infectious Diseases with Environmental Effects

In this paper, SIS and SIRS models for carrier dependent infectious diseases with immigration are proposed and analyzed by considering effects of environmental and human population related factors which are conducive to the growth of carrier population. In the modeling process, the density of carrier population is governed by a general logistic model. Further, it is assumed that the growth rate per capita and the modified carrying capacity of carrier population increase as the human population density increases. In each case, it is shown that the spread of an infectious disease increases as the carrier population density increases and the disease becomes more endemic due to immigration.

Effect of rain on removal of a gaseous pollutant and two different particulate matters from the atmosphere of a city

A nonlinear five-dimensional mathematical model is proposed and analyzed to study the removal of a gaseous pollutant and two different particulate matters by rain from the atmosphere of a city. The atmosphere, during rain, is assumed to consist of five interacting phases namely, the raindrops phase, the gaseous pollutant phase, its absorbed phase and the phases of two different particulate matters, one being formed by the gaseous pollutant. We assume that the gaseous pollutant is removed from the atmosphere by the processes of absorption while the two particulate matters are removed only by the process of impaction with different removal rates. By analyzing the model, it is shown that under appropriate conditions, these pollutants can be removed from the atmosphere and their equilibrium levels, remaining in the atmosphere, would depend mainly upon the rates of emission of pollutants, growth rate of raindrops, the rate of raindrops falling on the ground, etc. It is found that if the rates of conversion of gaseous pollutant into the particulate matter and rainfall are very large, then the gaseous pollutants would be removed completely from the atmosphere.

Characteristics of non-newtonian power law lubricants in step bearings and hydrostatic step seals

Abstract The effects of stepped film-thickness on the various characteristics of squeeze films, conical bearings and hydrostatic step seals, using a power law fluid as lubricant have been investigated. It has been shown that the load capacities of squeeze film bearings decrease and those of conical bearings and step seals increase, with the increase in the step height. With a hydrostatic step seal, the load capacity increases as the flow behaviour index of the power law fluid increases.

A new theory of lubrication for rough surfaces

Abstract A new theory of lubrication for rough surfaces is presented and a generalized form of the Reynolds equation is derived. A form of the Reynolds equation applicable to mixed lubrication conditions is obtained. In the case of a squeeze film it is shown that the load capacity increases as surface roughness increases.

Stability analysis and optimal control of an epidemic model with awareness programs by media

The impact of awareness campaigns and behavioral responses on epidemic outbreaks has been reported at times. However, to what extent does the provision of awareness and behavioral changes affect the epidemic trajectory is unknown, but important from the public health standpoint. To address this question, we formulate a mathematical model to study the effect of awareness campaigns by media on the outbreak of an epidemic. The awareness campaigns are treated as an intervention for the emergent disease. These awareness campaigns divide the whole populations into two subpopulation; aware and unaware, by inducing behavioral changes amongst them. The awareness campaigns are included explicitly as a separate dynamic variable in the modeling process. The model is analyzed qualitatively using stability theory of differential equations. We have also identified an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns, using optimal control theory. The control setting is investigated analytically using optimal control theory, and the numerical solutions illustrating the optimal regimens under various assumptions are also shown.

Externally pressurised porous thrust bearings with power law lubricants

Abstract A study of the characteristics of an externally pressurised porous thrust bearing revealed that the load capacity increases as the flow behaviour index n and the characteristics of the porous matrix increase.