Modelling and Analysis of Bacteria Dependent Infectious Diseases with Variable Contact Rates

In this research,we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases.It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives.In this model,we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat.The stability theory has been analyzed to analyzed to study the crucial role played by bacteria in the increased spread of an infectious disease.It is shown that as the density of non-emigrating population increases,the spread of an infectious disease increases.It is shown further that as the emigration increases,the spread of the disease decreases in both the cases of contact mentioned above rates,but this spread increases as these contact rates increase.It suggested that the control of bacteria in the human habitat is very useful to decrease the spread of an infectious disease.These results are confirmed by numerical simulation.

A MATHEMATICAL MODEL FOR THE DEPLETION OF FORESTRY RESOURCES DUE TO POPULATION AND POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

In this paper,a nonlinear mathematical model is proposed and analyzed to study the depletion of forestry resources caused simultaneously by population and population pressure augmented industrialization.The control of population pressure,using economic efforts is also considered in the modeling process.It is assumed that cumulative biomass density of forestry resources and the density of population follow logistic models.It is further assumed that the density of population and the level of industrialization increase as the cumulative biomass density of forestry resources increases.The cumulative density of economic efforts,which are applied to control the population pressure,is considered to be proportional to the population pressure.The model analysis shows that as the population pressure increases,the level of industrialization increases leading to decrease in the cumulative biomass density of forestry resources.It is found that if population pressure is controlled by using some economic efforts,the decrease in cumulative biomass density of forestry resources can be made much less than the case when no control is applied.It is also noted that if the population pressure augmented industrialization increases without control,the forestry resources may become extinct.