scholarly journals Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population

2003 ◽  
Vol 3 (2) ◽  
pp. 299-309 ◽  
Author(s):  
W.R. Derrick ◽  
◽  
P. van den Driessche ◽  
Keyword(s):  
Disease Transmission ◽  
Homoclinic Orbits ◽  
Transmission Model ◽  
Nonlinear Incidence ◽  
Disease Transmission Model

Lyapunov functions for a dengue disease transmission model

2009 ◽  
Vol 39 (2) ◽  
pp. 936-941 ◽  
Author(s):  
Jean Jules Tewa ◽  
Jean Luc Dimi ◽  
Samuel Bowong
Keyword(s):  
Disease Transmission ◽  
Lyapunov Functions ◽  
Transmission Model ◽  
Dengue Disease ◽  
Disease Transmission Model

Stability, Bifurcation and Optimal Control Analysis of a Malaria Model in a Periodic Environment

2018 ◽  
Vol 19 (6) ◽  
pp. 627-642 ◽  
Author(s):  
Prabir Panja ◽  
Shyamal Kumar Mondal ◽  
Joydev Chattopadhyay
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Existence Condition ◽  
Infected Mosquito ◽  
Transmission Model ◽  
Control Analysis ◽  
Periodic Environment ◽  
Vector Population ◽  
Autonomous Case ◽  
Disease Transmission Model

AbstractIn this paper, a malaria disease transmission model has been developed. Here, the disease transmission rates from mosquito to human as well as human to mosquito and death rate of infected mosquito have been constituted by two variabilities: one is periodicity with respect to time and another is based on some control parameters. Also, total vector population is divided into two subpopulations such as susceptible mosquito and infected mosquito as well as the total human population is divided into three subpopulations such as susceptible human, infected human and recovered human. The biologically feasible equilibria and their stability properties have been discussed. Again, the existence condition of the disease has been illustrated theoretically and numerically. Hopf-bifurcation analysis has been done numerically for autonomous case of our proposed model with respect to some important parameters. At last, a optimal control problem is formulated and solved using Pontryagin’s principle. In numerical simulations, different possible combination of controls have been illustrated including the comparisons of their effectiveness.

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