iosr-Jm   Volume-15 ~ Issue-6 ~ Nov – Dec 2019

Abstract: In this paper, in a host-parasite system that incorporates functional response and the growth rates would regulate the interaction among the species that might be induce the populations to approach steady states were investigated. To check the biological feasibility of the system, the positivity and boundedness of solutions of the model within deterministic environment are discussed. Moreover, the stability of equilibrium point of deterministic model is investigated. Finally, some numerical simulations to illustrate the analytical results were conducted........

Key Word: mathematical model; host-parasite; positivity and boundedness; equilibrium points; stability; Numerical simulation

[1]. May, R. M. & Anderson R, M. (1978). Regulation and stability of host-parasite population interactions: II. Destabilizing processes. Journal of Animal Ecology, 47, 249-67
[2]. Alyssa‑Lois M.( 2016). Non-native parasite enhances susceptibility of host to native predators, Springer-Verlag Berlin Heidelberg.
[3]. Hatcher MJ, Dick JTA, Dunn AM (2012).Disease emergence and invasions. Funct. Ecol 26:1275–1287.
[4]. J.H.P. Dawes and M.O. Souza (2013). A derivation of Holling's type I, II and III functional responses in predator-prey systems, 327, 11-22
[5]. E. Decaestecker.(2013). Damped long-term host-parasite Red Queen co- evolutionary dynamics: a reflection of dilution effects? Ecology Letters, 16: 1455-1462.

Abstract: In this paper, the evolution of traffic flow on the road intersection of a single lane three legs roundabout is analyzed from a macroscopic point of view following Lighthill–Whitham–Richards model. The single lane three legs roundabout is modeled as a sequence of 1×2 and 2×1 junctions. The priority parameter is introduced for 2×1 junctions to analyze the traffic evolution on the road network of the roundabout. Also, analyzed is the performance of the roundabout with and without priority parameter to evaluate the traffic evolution on the road network. Thereafter, the evolution of density and flux versus priority parameter at different time steps through numerical simulation using Godunov schemeis illustrated........

Key Word: Traffic flow, Priority Parameter, Roundabout, Traffic evolution, Numerical simulation.

[1] Alberto B., Fang Y.: Continuous Riemann Solvers for Traffic Flow at a Junction,Department of Mathematics, Penn State University, University Park, PA. 16802, U.S.A. (2014).
[2] Bergersen, B. D.: Numerical Solutions of Traffic Flow on Networks, Norwegian University of Science and Technology, 1, (2014).
[3] Colombo R. M.: Hyperbolic Phase Transitions in Traffic Flow, SIAM J. on Appl. Math., 63, (2002), 708-721.
[4] Colombo R. M., Goatin P., and Piccoli B.: Road network with phase transition, Journal of Hyperbolic Differential Equations, 7, (2010), 85-106.
[5] Courant R.,Friedrichs K., Lewy H.: On the partial difference equations of mathematical physics, IBM journal of Research and Development, 11(2), (1967), 215-234...

Abstract: This study targeted to analyze the relationship and stability between prey and predator Population with respect to impact of variable environment and harvesting factor on prey population. Prey-Predator concatenation is an authoritative and imperative discipline in analyzing and predicting population growth for future purposes and Management. The classical logistic growth model and Brody growth function of prey were applied to derive the corresponding predator's growth functions. Additionally, a coupled prey-predator's logistic model, variable carrying capacity with Holling's type II functional response and non selective harvest factor on prey population applied to account for sigmoid change of environment support. The effects of other model parameters presented using dynamic behavior of equilibrium points on prey-predator dynamics. The stability of the models presented analytically and by numerical simulation......

Keywords: Mathematical model, Prey-predator, Holling's type II Functional response, stability, variable carrying capacity, Non-selective Harvesting factor

[1]. H.Mohd Safuan et al, Coupled Logistic carrying capacity model ANZIAM J.53 (EMAC2011) pp.C172-C184, 2012
[2]. Mohammed Yiha Dawed et al , Mathematical modeling of population Growth: The case of logistic and Von Bertalanffy models open journal of modeling and simulation, 2014, 2,113-126.
[3]. Brody,S(1945) Bioenergetics and Growth Rheinhold Pub.corp.NY}
[4]. Peter.A.Abrams, Evolution of predator-prey interaction. Theory and evidence. Annual review of ecology and systematic 31(1):79-105 November 2000
[5]. Mariam.K.A1-Moqbali et al, Prey-predator models with Variable Carrying Capacity Mathematics 2018,6,102;doi:10.3390/math6060102

Abstract: In this study,amathematical modelof human population dynamicspertaining to the HIV/AIDShas been formulated. Thisstudy categorized human population into five compartments asSusceptible,Primary,Asymptomatic,Symptomatic,and AIDS (SPAJV). The well-possedness of the formulated models proved.The equilibrium points of the model are identified.Additionally, parametric expression for the basic reproduction number is constructedfollowing next generation matrix methodand analyzed its stability using Routh Hurwitz criterion. From the analytical and numerical simulation studies it is observed that if the basic reproduction is less than one unit then the solution converges to the disease free steady state i.e., disease will wipe out and thus the treatment is said to be successful.On the other hand, if the basic reproduction number is greater than one then the.......

Key Word: HIV, Basic Reproduction Number, Stability Analysis, Routh Hurwitz criterion, well-possedness

[1] Luboobi et al. 2011. The Role of HIV Positive Immigrants and Dual Protection in a Co-Infectionof Malaria and HIV/AIDS.Applied Mathematical Sciences, Vol. 5, 2011, no. 59, 2919 - 2942
[2] Vyambwer M.S., 2014. Mathematical modeling of the HIV/AIDS epidemic and the effect of public health education. M. Sc. Dissertation, Department of Mathematics and Applied Mathematics, University of the Western Cape.
[3] W.S. Ronald and H. James. Mathematical biology: An Introduction with Maple and Matlab. Springer Dordrecht Heidelberg, Boston, (1996).
[4] Koya, P.R., and Regassa K. 2019. Modeling and analysis of population dynamics of human cells pertaining to HIV/AIDS with treatment. American Journal of Applied Mathematics, doi: 10.11648/j.ajam.20190704.14
[5] Brauer F., P. van den Driessche and W. Jianhong. Mathematical Epidemiology, volume 1945. Springer-Verlag Berlin Heidelberg, Canada, 2008

Abstract: The optimal taxi pick-up for airport taxis is to save passengers' waiting for costs, reduce the no-load rate of taxis, and maximize the profit of taxi drivers in order to achieve reasonable allocation of traffic and people. For the first problem: Analyze the relevant decision-making factors affecting taxi drivers by using AHP and related analysis methods, and use Matlab to combine qualitative and quantitative analysis, systematic and hierarchical analysis, conduct consistency test and solve its weight. . For the second problem: Take Nanjing Lukou International Airport as an example, check the relevant information and collect the annual throughput of Lukou Airport as of 2018 and the number of taxis in Nanjing, simulate the simulation, and finally give the choice......

Key Word: Taxi scheduling;Analytic hierarchy process; Simulation; Queuing theory; ArcGIS

[1]. Jiang Qiyuan. Mathematical model [M]. January 2011, 4th edition. Higher Education Press, 1987: 252-253.
[2]. Yang Lifeng. Research on the organization and planning of landside road traffic in large airport terminal area [J]. Traffic and Transportation (Academic Edition), 2018 (01): 1-5..

Abstract: In this paper we developed a Modified Crank-Nicolson scheme for solving parabolic partial differential equations. The paper considers two solution methods for partial differential equations, one analytic and one numerical (finite difference method). The finite difference approximation, Modified Crank-Nicolson scheme, was implemented on the diffusion equation in order to solve it numerically. The aim was to compare exact solutions obtained by a classical method using separation of variables method, with the approximate solutions of Modified Crank-Nicolson method. Solutions of the numerical method were obtained manually since the method is easy and fast. The temperatures at specific time-steps were compared with their analytical result counterpart. The results were tabulated and presented also.

Key Word: Partial differential equation, Finite difference methods, Crank- Nicolson Method, Modified Crank-Nicolson Method, Parabolic Equations, Exact Solution. Mathematical Subject Classification: 35A20, 35A35, 35B35, 35K05

[1]. Crank J and Philis N. A practical method for Numerical Evaluation of solution of partial differential equation of heat conduction type. Proc. camb. Phil. soc. 1 (1996), 50-57
[2]. Cooper J. Introduction to Partial differential Equation with Matlab, Boston, 1958
[3]. Duffy D.J Finite difference methods in financial engineering. A Partial differential approach. Wiley, 2006
[4]. DuFort E.C and Franel S.P Conditions in Numerical treatment of Partial differential equations. Math. comput. 7(43) (1953): 135-152
[5]. Emenogu George Ndubueze and Oko Nlia Solutions of parabolic partial differential equations by finite difference methods. Jornal Applied Mathematics, 8(2) (2015): 88-102

Abstract: In this paper we deals non-instantaneous deteriorating items with multivariable demand which depend on selling price and available stock level. The rate of deterioration is constant which start after a certain time because items are non-instantaneous. Shortages are permitted and partially backlogged with fixed rate. The aim to develop this model is to find the optimal ordering quantity and optimal selling price. To illustrate the proposed model, a numerical example is carried out..

Key Word: Inventory, Deterioration, Multivariable demand, Partial Backlogging

[1]. Anupama Sharma, Vipin Kumar, Jyoti Singh, C.B.Gupta (2018) "Development of an Optimal Inventory Policy for Deteriorating Items with Stock Level and Selling Price Dependent Demand under Trade Credit" International Journal of Applied Engineering Research, Volume 13, Number 21 (2018) pp. 14861-14870
[2]. C.T. Yang, L.Y. Ouyang, H.H. Wu (2009) "Retailers optimal pricing and ordering policies for non-instantaneous deteriorating items with price-dependent demand and partial backlogging ", Mathematical Problems in Engineering.
[3]. Dye, C. Y. (2013). The effect of preservation technology investment on a non-Instantaneous deteriorating inventory model. Omega, 41(5), 872-880.
[4]. Ghare, P.M. and Schrader, G.F. (1963) "An inventory model for exponentially deteriorating items", Journal of Industrial Engineering, Vol. 14, pages 238–243.