Due to widespread applications, the multi-virus competing spreading dynamics has recently aroused considerable interests. To our knowledge, all previous competing spreading models assume infection rates that are each linear in the virus occupancy probabilities of the individuals in a population. As linear infection rates are overestimation of real infection rates, in some situations these models cannot accurately predict the spreading process of multiple competing viruses. This work takes the first step toward enhancing the accuracy of multi-virus competing spreading models. A continuous-time bilayer-network-based bi-virus competing spreading model with generic infection rates is proposed. Criteria for the extinction of both viruses and for the survival of only one virus are presented, respectively. Numerical examples show that (1) if the generic bi-virus spreading model with linear infection rates predicts that the fraction of nodes infected with some virus would approach zero, the prediction of the fraction is accurate, and (2) if the scenario-relevant generic infection rates could be estimated accurately, the resulting model would be able to accurately forecast the evolutionary process of a pair of competing viruses.

A Bi-Virus Competing Spreading Model with Generic Infection Rates

A Caputo–Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are investigated. The existence and uniqueness of the solution for the proposed FPWD model are given via the fixed point theorem. The numerical simulations for the model are obtained by using particular parameter values. The non-integer order derivative provides more flexible and deeper information about the complexity of the dynamics of the proposed FPWD model than the integer order models established before.

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A fractional order pine wilt disease model with Caputo–Fabrizio derivative

In this work, we investigate the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative. Moreover, with the use of fixed point theorem, the existence and uniqueness of the pine wilt disease model are obtained under Caputo operator. Using forward normalized sensitivity index, we determine the most sensitive parameters essential for the control of the infection and the results show that, decreasing the values of contact rate of a susceptible vector with infected pine trees and progression rate play a significant role in controlling the spread of pine wilt disease infection. On the other hand, we obtain different numerical simulations results of the model using the appropriate parameter values. Hence, from the graphs, it can be concluded that Caputo fractional operator gives more biologically observable behavior of the proposed disease model thanks to the changed fractional order. Compared to the previously built integer order model, the non-integer order derivative provided more efficient and flexible information about the complexity of the model’s dynamics.

Mathematical modeling of pine wilt disease with Caputo fractional operator

This paper presents and examine a mathematical system of equations which describes the dynamics of pine wilt disease (PWD) Firstly, we examine the model with constant controls Here, we investigate the disease equilibria and calculate the basic reproduction number of the disease Secondly, we incorporate time dependent controls into the model and then analyze the conditions that are necessary for the disease to be controlled optimally Finally, the numerical results for the model are presented

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Mathematical modeling and stability analysis of Pine Wilt Disease with optimal control.

The present studies provide qualitative aspects of pine wilt disease model while incorporating convex incidence rate. Studying the nature of the proposed model, it is shown that the basic reproductive number completely determine various dynamics of the model. The global asymptotic stability analysis is expounded at different equilibrium points. The model has shown that the disease disappear, when the threshold quantity falls below unity. Numerical results are presented graphically to illustrate theoretical discussions.

Host vector dynamics of pine wilt disease model with convex incidence rate

We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction number and investigate the stability of a disease-free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction number . We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree-injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree-injection strategy for controlling the spread of PWD.

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Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

Based on classical epidemic models, this paper considers a deterministic epidemic model for the spread of the pine wilt disease which has vector mediated transmission. The analysis of the model shows that its dynamics are completely determined by the basic reproduction number . Using a Lyapunov function and a LaSalle's invariant set theorem, we proved the global asymptotical stability of the disease-free equilibrium. We find that if , the disease free equilibrium is globally asymptotically stable, and the disease will be eliminated. If , a unique endemic equilibrium exists and is shown to be globally asymptotically stable, under certain restrictions on the parameter values, using the geometric approach method for global stability, due to Li and Muldowney and the disease persists at the endemic equilibrium state if it initially exists.

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Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate

A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for t ...

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Kwang Sung Lee

Papers

Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

Global Stability of a Host-Vector Model for Pine Wilt Disease with Nonlinear Incidence Rate

Stability analysis of a host-vector transmission model for pine wilt disease with asymptomatic carrier trees