One tuberculosis transmission model is formulated by incorporating exogenous reinfec- tion, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obta...One tuberculosis transmission model is formulated by incorporating exogenous reinfec- tion, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.展开更多
Migration of infected animals and humans,and mutation are considered as the source of the introduction of new pathogens and strains into a country.In this paper,we formulate a mathematical model of Ebola virus disease...Migration of infected animals and humans,and mutation are considered as the source of the introduction of new pathogens and strains into a country.In this paper,we formulate a mathematical model of Ebola virus disease dynamics,that describes the introduction of a new strain of ebolavirus,through either mutation or immigration(which can be continuous or impulsive)of infectives.The mathematical analysis of the model shows that when the immigration of infectives is continuous,the new strain invades a country if its invasion reproduction number is greater than one.When the immigration is impulsive,a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist.This ratio is one if the population size is constant.In case of mutation of the resident strain of ebolavirus,the coexistence of the resident and mutated strains is possible at least if their respective reproduction numbers are greater than one.Results indicate that the competition for the susceptible population is the immediate consequence of the coexistence of two different strains of ebolavirus in a country and this competition is favourable to the most infectious strain.Results also indicate that impulsive immigration of infectives when compared with continuous immigration of infectives gives time for the implementation of control measures.Our model results suggest controlled movements of people between countries that have had Ebola outbreaks despite the fact that closing boundaries is impossible.展开更多
In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the mod...In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria （including the disease free equilibrium, dominant equilibria and the coexistence equilibrium） is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.展开更多
文摘One tuberculosis transmission model is formulated by incorporating exogenous reinfec- tion, relapse, and two treatment stages of infectious TB cases. The global stability of the unique disease-free equilibrium is obtained by applying the comparison principle if the effective reproduction number for the full model is less than unity. The existence and stability of the boundary equilibria are given by introducing the invasion reproduction numbers. Furthermore, the existence and local stability of the endemic equilibrium are addressed under some conditions.
文摘Migration of infected animals and humans,and mutation are considered as the source of the introduction of new pathogens and strains into a country.In this paper,we formulate a mathematical model of Ebola virus disease dynamics,that describes the introduction of a new strain of ebolavirus,through either mutation or immigration(which can be continuous or impulsive)of infectives.The mathematical analysis of the model shows that when the immigration of infectives is continuous,the new strain invades a country if its invasion reproduction number is greater than one.When the immigration is impulsive,a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist.This ratio is one if the population size is constant.In case of mutation of the resident strain of ebolavirus,the coexistence of the resident and mutated strains is possible at least if their respective reproduction numbers are greater than one.Results indicate that the competition for the susceptible population is the immediate consequence of the coexistence of two different strains of ebolavirus in a country and this competition is favourable to the most infectious strain.Results also indicate that impulsive immigration of infectives when compared with continuous immigration of infectives gives time for the implementation of control measures.Our model results suggest controlled movements of people between countries that have had Ebola outbreaks despite the fact that closing boundaries is impossible.
文摘In this paper, we propose a two strain epidemic model with single host population. It is assumed that strain one can mutate into strain two. Also latent-stage progression age and mutation are incorporated into the model. Stability of equilibria （including the disease free equilibrium, dominant equilibria and the coexistence equilibrium） is investigated and it is found that they are locally stable under suitable and biological feasible constraints. Results indicate that the competition exclusion and coexistence of the two strains are possible depending on the mutation. Numerical simulations are also performed to illustrate these results.
