Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resist...Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant tuberculosis). In this work, we extend the standard SEIRS epidemiology model of tuberculosis to include MDR-TB. For that, we considered compartments of susceptible, exposed, infected, resistant to a first line of treatment and recovered humans and we modeled the natural growth, the interactions between these populations and the effects of treatments. We calculate the basic reproduction number, , using the next generation method. The DFE and the EE are established and their stability analysis done to show that they are locally and globally asymptotically stable. Numerical analysis for the model with and without delay is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will still persist due to lack of permanent immunity to tuberculosis while the recovered can still lose their immunity to become susceptible again.展开更多
In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place t...In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number R <sub>0</sub> is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if R <sub>0</sub> ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if R <sub>0</sub> > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduction number and to the level of the endemic equilibrium is analyzed.展开更多
We consider a rift valley fever model with treatment in human and livestock populations and trapping in the vector (mosquito) population. The basic reproduction number R <sub>0</sub> is established and use...We consider a rift valley fever model with treatment in human and livestock populations and trapping in the vector (mosquito) population. The basic reproduction number R <sub>0</sub> is established and used to determine whether the disease dies out or is established in the three populations. When R <sub>0</sub> ≤ 1, the disease-free equilibrium is shown to be globally asymptotically stable and the disease does not spread and when R <sub>0</sub> > 1, a unique endemic equilibrium exists which is globally stable and the disease will spread. The mathematical model is analyzed analytically and numerically to obtain insight of the impact of intervention in reducing the burden of rift valley fever disease’s spread or epidemic and also to determine factors influencing the outcome of the epidemic. Sensitivity analysis for key parameters is also done.展开更多
文摘Despite the enormous progress in prevention and treatment, tuberculosis disease remains a leading cause of death worldwide and one of the major sources of concern is the drug resistant strain, MDR-TB (multidrug resistant tuberculosis) and XDR-TB (extensively drug resistant tuberculosis). In this work, we extend the standard SEIRS epidemiology model of tuberculosis to include MDR-TB. For that, we considered compartments of susceptible, exposed, infected, resistant to a first line of treatment and recovered humans and we modeled the natural growth, the interactions between these populations and the effects of treatments. We calculate the basic reproduction number, , using the next generation method. The DFE and the EE are established and their stability analysis done to show that they are locally and globally asymptotically stable. Numerical analysis for the model with and without delay is done and demonstrated that in the case of patients with both active tuberculosis and MDR tuberculosis, both strains will still persist due to lack of permanent immunity to tuberculosis while the recovered can still lose their immunity to become susceptible again.
文摘In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number R <sub>0</sub> is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if R <sub>0</sub> ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if R <sub>0</sub> > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduction number and to the level of the endemic equilibrium is analyzed.
文摘We consider a rift valley fever model with treatment in human and livestock populations and trapping in the vector (mosquito) population. The basic reproduction number R <sub>0</sub> is established and used to determine whether the disease dies out or is established in the three populations. When R <sub>0</sub> ≤ 1, the disease-free equilibrium is shown to be globally asymptotically stable and the disease does not spread and when R <sub>0</sub> > 1, a unique endemic equilibrium exists which is globally stable and the disease will spread. The mathematical model is analyzed analytically and numerically to obtain insight of the impact of intervention in reducing the burden of rift valley fever disease’s spread or epidemic and also to determine factors influencing the outcome of the epidemic. Sensitivity analysis for key parameters is also done.
