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A mathematical model for the dynamics and MCMC analysis of tomato bacterial wilt disease

International Journal of Biomathematics 2018年第1期11卷 1-22页

作者： Flavia Remo Livingstone S. Luboobi isambi sailon mabalawata Betty K. Nannyonga Institut fiir Mathematik Friedrich Schiller University Jena Ernst-Abbe-Platz 2 Jena 07743 Germany Department of Mathematics Makerere University P. O. Box 7062 Kampala Uganda African Institute of Mathematical Sciences (AIMS) Tanzania P. O. Box 176 Bagamoyo -- Coastal Region Tanzania

In this paper, we formulate and analyze a mathematical model to investigate the trans- mission dynamics of tomato bacterial wilt disease （TBWD） in Mukono district, Uganda. We derive the basic reproduction number R0 and prove the existence of a disease- free equilibrium point which is globally stable if R0 〈 1 and an endemic equilibrium which exists if R0 〉 1. Model parameters are estimated using the Markov Chain Monte Carlo （MCMC） methods and robustness tested. The model parameters were observed to be identifiable. Numerical simulations show that soil solarization and sensitization of

关键词：数学模型西红柿动力学 MCMC 疾病枯萎细菌模型参数

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Stochastic Dynamics of Cholera Epidemic Model: Formulation, Analysis and Numerical Simulation

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Journal of Applied Mathematics and Physics 2019年第5期7卷 1097-1125页

作者： Yohana Maiga Marwa isambi sailon Mbalawata Samuel Mwalili Wilson Mahera Charles Mathematics and Statistics Department Institute for Basic SciencesTechnology and InnovationPan African UniversityNairobiKenya Tanzania Public Service College SingidaTanzania African Institute for Mathematical Sciences Dar es SalaamTanzania Jomo Kenyatta University of Agriculture and Technology NairobiKenya University of Dar es Salaam Dar es SalaamTanzania

In this paper, we describe the two different stochastic differential equations representing cholera dynamics. The first stochastic differential equation is formulated by introducing the stochasticity to deterministic model by parametric perturbation technique which is a standard technique in stochastic modeling and the second stochastic differential equation is formulated using transition probabilities. We analyse a stochastic model using suitable Lyapunov function and Itôformula. We state and prove the conditions for global existence, uniqueness of positive solutions, stochastic boundedness, global stability in probability, moment exponential stability, and almost sure convergence. We also carry out numerical simulation using Euler-Maruyama scheme to simulate the sample paths of stochastic differential equations. Our results show that the sample paths are continuous but not differentiable (a property of Wiener process). Also, we compare the numerical simulation results for deterministic and stochastic models. We find that the sample path of SIsIaR-B stochastic differential equations model fluctuates within the solution of the SIsIaR-B ordinary differential equation model. Furthermore, we use extended Kalman filter to estimate the model compartments (states), we find that the state estimates fit the measurements. Maximum likelihood estimation method for estimating the model parameters is also discussed.

关键词： Stochastic Differential Equations Stability Condition Extended Kalman Filter Ito Formula Lyapunov Function Euler-Maruyama Scheme

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