Modeling the impact of migrated population on human-to-human transmission of Ebola virus disease

A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of the dynamics of Ebola virus disease,here,the infected class is supposed to be divided into subclasses,viz.primary and secondary infected.The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation.The obtained results,qualitatively and quantitatively,suggest that migration and contact rates play an important role in controlling the spreading of disease.Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values,it leads to delay in the stabilization of the system.It is also found that primary reproductive number increases with increase in migration rate.Besides this,the approximate time required to attain stability of the disease model system is also determined.The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.

Modeling the effects of environmental pollution intensified by urbanization on human population

A mathematical model is presented here to investigate the effects of environmental pollution,intensified by urbanization,on the density of human population.Here,urbanization is assumed to grow with constant rate and also,induced through growing population and the corresponding population pressure.The model analysis,qualitatively and numerically,show that though the growth of population or population pressure is responsible for the growing urbanization,but for very large increase of urbanization,the population may not survive in the long run due to environmental pollution driven by urbanization.

A NUMERICAL APPROACH STUDYING THE EFFECTS OF PRECIPITATION SCAVENGING ON STEADY-STATE DISPERSION OF AIR POLLUTANTS

The present paper demonstrates the applicability of finite element method of weighted residuals to study the effects of precipitation scavenging through raindrops on the steady-state dispersion of air pollutants in the atmosphere under realistic variable wind and diffusivity profiles.Here,the washout of pollutants by rain droplets is considered and the whole analysis for the pollutant concentration is carried out in two phases viz.gaseous phase and droplet phase.The model solutions are obtained by using local basis and asymmetric quadratic weighting functions which can provide a promising alternative to the standard Galerkin formulation for problems with advective and diffusive terms.The results of the model reveal that the precipitation scavenging by rain is quite effective in cleaning the polluted atmosphere.Anticipating the need of pollutant concentration in rain drops regarding acid precipitation(or acid rain),the concentration of the absorbed pollutant in the droplet phase are also analyzed.So,the present study provides an understanding on the concentration distribution of pollutant in gaseous and droplet phases,under the effects of variable wind and diffusivity profiles.

Transmission dynamics of depression in socially connected population: A nonlinear modeling study

Human emotions are considered to be contagious that can be transmitted from one person to another during social interactions.However,interaction with people having excessive negative emotions may make other people depressed.Taking this aspect into consideration,a SIR nonlinear model is formulated to investigate the transmission dynamics of depression in social connections.Through qualitative analysis of the model,critical value of depression is determined.Two equilibria,viz.depression free and depression state,are obtained and their stability behaviors are analyzed.The stability analysis reveals the fact that both the equilibria are locally and globally stable,depending on critical value of depression.The sensitivity analysis of crucial parameters of critical value of depression is performed to point out the key parameters that can drastically influence the propagation of depression.The results demonstrate the importance of counselling for depressed persons in order to suppress the growth of depression in social connections.The model calibration has been done for the annual depression cases of Zimbabwe.The results of our study show that individuals will catch major depression disorders more quickly once they get initially(primary)depressed.For this,counselling rate for primary depressed population should be increased.