O. Misra - Academia.edu (original) (raw)

Volume 1 Issue 2 by O. Misra

In this paper, a mathematical model is proposed and analyzed to study the effect of toxicant in a... more In this paper, a mathematical model is proposed and analyzed to study the effect of toxicant in a three species
food chain system with “food-limited” growth of prey population. The mathematical model is formulated using the
system of non-linear ordinary differential equations. In the model, there are seven state variables, viz, prey density,
intermediate predator density, density of top predator, concentration of toxicant in the environment, concentration
of toxicant in the prey, concentration of toxicant in the intermediate predator and concentration of toxicant in
the top predator. In the model, it is assumed that the carrying capacity and growth rate of prey is affected by
environmental toxicant. Toxicant is transferred to intermediate predator and top predator populations through
food chain pathways. All the feasible equilibria of the system are obtained and the conditions are determined for
the survival or extinction of species under the effect of toxicant. The local and global stability analysis of all the
feasible equilibria are carried out. Further, the results are compared with the case when toxicant is absent in the
system. Finally, we support our analytical findings with numerical simulations.

Papers by O. Misra

International Journal of Modeling, Simulation, and Scientific Computing

A mathematical model is proposed in this paper to study the transmission and control of COVID-19.... more A mathematical model is proposed in this paper to study the transmission and control of COVID-19. The mathematical model is formulated using system of nonlinear ordinary differential equations. The model includes disease-related parameters such as contact rate, disease-induced death rates, immigration rate and transition rates along with parameters for control measures such as implementation of social distancing practices, isolation and quarantine rates. From the stability analysis of the model, it is shown that if the social distancing is practiced by the large number of susceptible population, then the disease will not spread, and it may eventually die out. Further, it is derived from the analysis of the model that if most of the infected populations are isolated or quarantined, then the spread of the disease can be eventually controlled. However, from the analysis of the model, it is observed that if there is constant immigration of asymptomatic infected persons, then the disease...

Journal of Applied Mathematics and Computing

Journal of Nonlinear Sciences and Applications

A mathematical model is proposed to study the simultaneous effects of toxicant and infectious dis... more A mathematical model is proposed to study the simultaneous effects of toxicant and infectious disease on Lotka-Volterra prey-predator system. It is considered in the model that only the prey population is being affected by disease and toxicant both, and the susceptible and infected prey populations are being predated by predator. All the feasible equilibrium of the model are obtained and the condition for the existence of interior equilibrium point is also been determined. The criteria for both local stability and instability involving ecotoxicological and epidemiological parameters are derived. The global stability of the interior equilibrium point is discussed using Lyapunov's direct method. The results are compared with the case when environmental toxicant is absent. Moreover, threshold conditions depending upon toxicant, disease and predation related parameters for the non-linear stability of the model is determined. Finally, the numerical verifications of analytic results are carried out.

International Journal of Applied and Computational Mathematics

Nonlinear Analysis: Hybrid Systems

Although vaccination is a highly effective method of preventing infections, one dose of vaccine d... more Although vaccination is a highly effective method of preventing infections, one dose of vaccine does not protect all recipients. Natural infection with diseases induces permanent immunity whereas vaccine induced immunity has a temporary effect. The reduction in vaccine induced immunity leads us to introduce a booster programme. A mathematical model that can be used to study the effect of multiple

International Journal of Applied and Computational Mathematics

Modeling Earth Systems and Environment, 2016

In this paper, the effect of toxicant on the dynamics of Leslie-Gower tritrophic food chain popul... more In this paper, the effect of toxicant on the dynamics of Leslie-Gower tritrophic food chain population model is studied. Two models have been studied to visualize the dynamical behaviour of prey and predator populations under toxicant stress. All the feasible equilibria of the systems are obtained and using stability theory the conditions are derived for the survival or extinction of species. From the analysis of the models it is observed that the effect of toxicant on predator population increases the equilibrium density of prey population. Finally, we support our analytical findings with numerical simulations.

Modeling Earth Systems and Environment, 2016

In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of ... more In this paper, a nonlinear mathematical model is proposed and analyzed to study the depletion of dissolved oxygen and survival or extinction of fish population in a nutrient enriched aquatic ecosystem. It is assumed in the model that there is an external constant input of nutrients (phosphorus and nitrogen) in the water body on account of anthropogenic activities. Stability analysis of the equilibria of the model is carried out and from the analysis it is shown that the fish population will survive at very low equilibrium level due to reduced concentration of dissolved oxygen and excessive presence of algal biomass on account of nutrient loading. Further, it is shown in this paper that the fish population tend to extinction due to decrease in the concentration of dissolved oxygen from its threshold level. Numerical simulations are also carried out in this paper to support the analytical results.

Thermal pollutants include the waste heat chiefly from atomic, nuclear and thermal power plants, ... more Thermal pollutants include the waste heat chiefly from atomic, nuclear and thermal power plants, which adversely affect the aquatic environment. Coal fired or nuclear fuel-fired steam power plants are associated with the problem of thermal pollution. The study of the effects of temperature on the existence of resource based predator-prey system is carried out in the paper using mathematical model. The study has been conducted considering prey-predator system in which the parameters like growth rate, death rate, carrying capacity and interaction coefficients are assumed to be the functions of temperature which itself is changing with time. In writing the model, a separate dynamical equation for the temperature is supplemented with the equations for prey-predator system. In this paper, the effect of temperature is assumed to occur due to the natural reasons such as seasonal or climatic changes and also as a result of the hot water discharge from the industries. The mathematical model ...

The modeling investigation in this paper discusses the system level effects of a toxicant on a th... more The modeling investigation in this paper discusses the system level effects of a toxicant on a three species food chain system and the state variables of the models are prey and predator densities, concentration of toxicant in the environment and the concentration of toxicant in the prey population. In the models, we have assumed that the presence of top predator reduces the predatory ability of the intermediate predator. The stability analysis of the models is carried out and the sufficient conditions for the existence and extinction of the populations under the stress of toxicant are obtained. Further, it is also found that the predation rate of the intermediate predator is a bifurcating parameter and Hopf-bifurcation occurs at some critical value of this parameter. Finally, numerical simulation is carried out to support the analytical results.

Indian Journal of Pure and Applied Mathematics

We study a mathematical model of an egg-eating predator-prey interaction consisting of age struct... more We study a mathematical model of an egg-eating predator-prey interaction consisting of age structures in both the populations of prey and predators. In constructing the model, it is assumed that the birth of predators depends on all previous egg levels of prey, and the model is constructed by considering two age groups in the predator population. For the prey population, a continuous time and age scale model is considered, whereas for the predator population a continuous time and a discrete age scale model is considered. The linear stability analysis of the equilibria of the model are conducted for some special cases taking particular forms of fecundity rates and weight functions. It is shown from these analyses that if the net reproductive rates of the prey species are greater than one, then both of the species will co-exist.

Proceedings of the National Academy of Sciences, India - Section A

A mathematical model has been presented to study the growth of infection taking into account expl... more A mathematical model has been presented to study the growth of infection taking into account explicitly the dynamics of parasite population growth and defence mechanism of the immune system. The model is analysed by determining the equilibria and their stability. Particular emphasis has been placed on the influence of immunity and parasite dynamics on the growth of infection; and a stability condition has been obtained in order to determine the growth and existence of the disease.

A mathematical model is proposed to study the effect of soil pollution on the growth dynamics of ... more A mathematical model is proposed to study the effect of soil pollution on the growth dynamics of plant-herbivore systems. In the model the plant biomass is divided into two compartments consisting of leaves and roots. In the modeling process, it has been assumed that the pollution in the soil causes damage to the root compartment, thereby destroying the substrates in the soil that causes damage to the root compartment and destroying the substrates in this compartment. Also it is assumed that the pollutant is being transferred from the root compartment to the leaf compartment which in turn adversely affects the substrates in this compartment also. Since the growth of plant biomass in both the compartments depend on the substrate concentration, the weight of the leaf and root compartments of plant biomass decrease on account of the polluted soil. A separate equation has been considered to study the dynamics of the herbivore population. A stability analysis of the two equilibrium point...

This paper aims to study a SIR model with and without vaccination. A reproduction number R0 is de... more This paper aims to study a SIR model with and without vaccination. A reproduction number R0 is defined and it is obtained that the disease-free equilibrium point is unstable if 𝑅𝑅0>1 and the non-trivial endemic equilibrium point exist if 𝑅𝑅0>1 in the absence of vaccination. Further, a new reproduction number 𝑅𝑅𝑣𝑣 is defined for the model in which vaccination is introduced. The linear stability and the global stability of both the models are discussed and the comparison of both the models is done regarding the existence of the disease-free equilibrium point and endemic equilibrium point. Finally, a numerical example is given in support of the result.

The Indian journal of surgery, 1949

Journal Applied Mathematics, 2012

Chikungunya is a vector borne communicab le disease which is transmitted in human population thro... more Chikungunya is a vector borne communicab le disease which is transmitted in human population through the bite of an infected Aedes-Aegeypti mosquito. In order to study the spread of Chikungunya disease a model has been proposed and analyzed in this paper. In the proposed model the human population and the mosquito population have been divided into three and two classes respectively. For controlling the disease, vector control measures such as, reduction in the breeding of vector population, killing of mosquitoes and isolation of infected humans have been also taken in to account in the model. Linear and non-linear stability analysis of the model has been carried out. Fro m the analysis we have derived a threshold condition involving control reproductive number , and we have found that the disease free equilibriu m point is locally asymptotically stable when and unstable when .We have also proved that a unique endemic equilibriu m point exists and is locally asymptotically stable when. Thus, we have concluded from the analysis of the model that the disease will either die out or will remain endemic depending on the value of control reproductive number. This study will assist the health department in controlling the spread of Chikungunya disease by introducing the control measures such as increasing the awareness in the society, killing of mosquitoes and isolating the infected individuals.

International Journal of Modeling, Simulation, and Scientific Computing

Journal of Applied Mathematics and Computing

Journal of Nonlinear Sciences and Applications

International Journal of Applied and Computational Mathematics

Nonlinear Analysis: Hybrid Systems

International Journal of Applied and Computational Mathematics

Modeling Earth Systems and Environment, 2016

Indian Journal of Pure and Applied Mathematics

Proceedings of the National Academy of Sciences, India - Section A

The Indian journal of surgery, 1949

Journal Applied Mathematics, 2012

International Journal of Biomathematics, 2015

Animals grouping together is one of the most interesting phenomena in population dynamics and dif... more Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey–predator forming groups have been considered by many authors in their models. In the present paper we have considered a model for one prey and two competing predator populations with time lag and square root functional response on account of herd formation by prey. It is shown that due to the inclusion of another competing predator, the underlying system without delay becomes more stable and limit cycles do not occur naturally. However, after considering the effect of time lag in the basic system, limit cycles appear in the case of all equilibrium points when delay time crosses some critical value. From the numerical simulation, it is observed that the length of delay is minimum when only prey population survives and it is maximum when all the populations coexist.