Ram Naresh

Modeling the effect of screening of unaware infectives on the spread of HIV infection

In this paper, a non-linear mathematical model is proposed and analyzed to study the effect of screening of unaware infectives on the spread of HIV/AIDS in a homogeneous population with constant immigration of susceptibles. In modeling the dynamics, the population is divided into four subclasses of HIV negatives but susceptibles, HIV positives or infectives that do not know they are infected, HIV positives that know they are infected and that of AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives and all infectives move with a constant rate to develop AIDS. The model is analyzed by using the stability theory of differential equations and numerical simulation. The model analysis shows that screening of unaware infectives has the effect of reducing the spread of the AIDS epidemic in a homogeneous population with migration. It is noted that the endemicity of the infection is reduced when infectives after becoming aware of their infection do not take part in sexual interaction whereas it increases in the absence of screening of unaware infectives. The model analysis has also been applied to compare the theoretical results with the known Indian HIV data.

Modelling and analysis of the spread of AIDS epidemic with immigration of HIV infectives

We propose and analyze, a nonlinear mathematical model of the spread of HIV/AIDS in a population of varying size with immigration of infectives. It is assumed that susceptibles become infected via sexual contacts with infectives (also assumed to be infectious) and all infectives ultimately develop AIDS. The model is studied using stability theory of differential equations and computer simulation. Model dynamics is also discussed under two particular cases when there is no direct inflow of infectives. On analyzing these situations, it is found that the disease is always persistent if the direct immigration of infectives is allowed in the community. Further, in the absence of inflow of infectives, the endemicity of the disease is found to be higher if pre-AIDS individuals also interact sexually in comparison to the case when they do not take part in sexual interactions. Thus, if the direct immigration of infectives is restricted, the spread of infection can be slowed down. A numerical study of the model is also carried out to investigate the influence of certain key parameters on the spread of the disease.

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.

A nonlinear AIDS epidemic model with screening and time delay

Abstract A nonlinear mathematical model to study the effect of time delay in the recruitment of infected persons on the transmission dynamics of HIV/AIDS is proposed and analyzed. In modeling the dynamics, the population is divided into four subclasses: the susceptibles, the HIV positives or infectives that do not know they are infected, the HIV positives that know they are infected and the AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives. The model is analyzed using stability theory of delay differential equations. Both the disease-free and the endemic equilibria are found and their stability is investigated. It is shown that the introduction of time delay in the model has a destabilizing effect on the system and periodic solutions can arise by Hopf bifurcation. Numerical simulations are also carried out to investigate the influence of key parameters on the spread of the disease, to support the analytical conclusion and to illustrate possible behavioral scenario of the model.

Modeling the effect of an intermediate toxic product formed by uptake of a toxicant on plant biomass

In this paper, a nonlinear mathematical model is proposed and analyzed to study the effect of an intermediate toxic product on the growth of plant biomass. It is assumed that the toxicant uptaken by plant biomass interacts with water (sap) present in it and forms an intermediate product, which then affects the biomass. To model the phenomena, it is further assumed that the intermediate product decreases the intrinsic growth rate of biomass density while the environmental concentration of toxicant decreases its carrying capacity. The model is analyzed using stability theory of differential equations and numerical simulation. It is shown that as the rate of emission of toxicant increases, the equilibrium level of plant biomass decreases, but this effect is determined by the emission rate of toxicant in the environment, the rate of its uptake as well as by the rate of formation of the intermediate toxic product.

Modeling the effect of time delay in controlling the carrier dependent infectious disease – Cholera

Abstract A delay mathematical model for the control of cholera epidemic is proposed and analyzed. It is assumed that the disease spreads through carriers, which makes the human food contaminated by transporting bacteria from the environment. It is also assumed that insecticides are used to control the carriers with the rate proportional to the density of carriers. The analysis of model shows that the disease may be controlled by spraying insecticides but a longer delay in spraying insecticides may destabilize the system. Simulation is also carried out to support the analytical results.

Qualitative Analysis of a Nonlinear Model for Removal of Air Pollutants

A nonlinear mathematical model is proposed to study the removal of air pollutants by precipitation in the atmosphere. The atmosphere, under consideration, consists of three interacting phases i.e. the droplet phase, the pollutant phase, and the phase of pollutants absorbed in the droplets. The dynamics of these phases is governed by the ordinary differential equations with source, nonlinear interaction and removal terms. The proposed model is analyzed qualitatively using stability theory. It is shown that under appropriate conditions, the pollutants can be washed out from the atmosphere significantly and the removed amount would depend upon the rate of introduction of pollutants, rate of precipitation, rate of absorption, and rate of falling droplets on the ground. The results are found to be in line with the experimental observations published in the literature.

Removal of carbon dioxide from the atmosphere to reduce global warming: a modelling study

We propose non–linear models to study the feasibility of removing CO2 from the atmosphere by introducing some external species such as liquid droplets and particulate matters in the atmosphere, which may react with this gas and get it removed by gravity. Further, this gas can also be removed by photosynthesis process upon using plantation of leafy trees around the sources of emission. The proposed nonlinear models are analysed using stability theory of differential equations and computer simulations. Model analysis suggests that the concentration of global warming gas decreases as the rates of introduction of liquid droplets and particulate matters increase. Also, this gas can be removed almost completely from the atmosphere, if the rates of introduction of these external species are very large. The concentration of CO2 also decreases as its absorption by green belt increases. It decreases further if the rate of introduction of external species increases. The numerical simulation of the models confirms these analytical results.

MODELING THE CUMULATIVE EFFECT OF ECOLOGICAL FACTORS IN THE HABITAT ON THE SPREAD OF TUBERCULOSIS

In this paper, the cumulative effect of ecological factors in the habitat on the spread of tuberculosis (TB) in human population is modeled and analyzed. The total human population is divided into two classes, susceptibles and infectives. It is assumed that TB is not only spread by direct contacts with infectives in the population but also indirectly by bacteria which are emitted by infectives in the habitat. It is assumed further that bacteria survive due to conducive ecological factors such as flower pots, plants, grasses, human clothes, etc. in the habitat. The cumulative density of ecological factors in the habitat is assumed to be governed by a population density dependent logistic model. The analysis of the model shows that as parameters governing the conducive ecological factors in the habitat increase, the spread of TB increases. The same result is also found with the increase in the parameter governing the survival and accumulation of bacteria in the habitat. It is further found that due to immigration of the population TB becomes more endemic. A numerical study of the model is also carried out to support the analytical results.

A nonlinear HIV/AIDS model with contact tracing

A nonlinear mathematical model is proposed and analyzed to study the effect of contact tracing on reducing the spread of HIV/AIDS in a homogeneous population with constant immigration of susceptibles. In modeling the dynamics, the population is divided into four subclasses of HIV negatives but susceptibles, HIV positives or infectives that do not know they are infected, HIV positives that know they are infected and that of AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives and all infectives move with constant rates to develop AIDS. The model is analyzed using the stability theory of differential equations and numerical simulation. The model analysis shows that contact tracing may be of immense help in reducing the spread of AIDS epidemic in a population. It is also found that the endemicity of infection is reduced when infectives after becoming aware of their infection do not take part in sexual interaction.