A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed.The model is shown to exhibit the phenomenon of backward bifurcation,where a stable disease-free ...A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed.The model is shown to exhibit the phenomenon of backward bifurcation,where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number R_(0) is less than one.It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse.The existence of backward bifurcation implies that bringing down R_(0) to less than unity is not enough for disease eradication.In the absence of backward bifurcation,the global asymptotic stability of the disease-free equilibrium is shown whenever R_(0)<1.For R_(0)>1,the existence of at least one locally asymptotically stable endemic equilibrium is shown.Sensitivity analysis of the model,using the parameters relevant to the transmission dynamics of the melioidosis disease,is discussed.Numerical experiments are presented to support the theoretical analysis of the model.In the numerical experimentations,it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.展开更多
Malaria infection continues to be a major problem in many parts of the world including Africa.Environmental variables are known to significantly affect the population dynamics and abundance of insects,major catalysts ...Malaria infection continues to be a major problem in many parts of the world including Africa.Environmental variables are known to significantly affect the population dynamics and abundance of insects,major catalysts of vector-borne diseases,but the exact extent and consequences of this sensitivity are not yet well established.To assess the impact of the variability in temperature and rainfall on the transmission dynamics of malaria in a population,we propose a model consisting of a system of non-autonomous deterministic equations that incorporate the effect of both temperature and rainfall to the dispersion and mortality rate of adult mosquitoes.The model has been validated using epidemiological data collected from the western region of Ethiopia by considering the trends for the cases of malaria and the climate variation in the region.Further,a mathematical analysis is performed to assess the impact of temperature and rainfall change on the transmission dynamics of the model.The periodic variation of seasonal variables as well as the non-periodic variation due to the long-term climate variation have been incorporated and analyzed.In both periodic and non-periodic cases,it has been shown that the disease-free solution of the model is globally asymptotically stable when the basic reproduction ratio is less than unity in the periodic system and when the threshold function is less than unity in the non-periodic system.The disease is uniformly persistent when the basic reproduction ratio is greater than unity in the periodic system and when the threshold function is greater than unity in the non-periodic system.展开更多
文摘A deterministic model for the transmission dynamics of melioidosis disease in human population is designed and analyzed.The model is shown to exhibit the phenomenon of backward bifurcation,where a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the basic reproduction number R_(0) is less than one.It is further shown that the backward bifurcation dynamics is caused by the reinfection of individuals who recovered from the disease and relapse.The existence of backward bifurcation implies that bringing down R_(0) to less than unity is not enough for disease eradication.In the absence of backward bifurcation,the global asymptotic stability of the disease-free equilibrium is shown whenever R_(0)<1.For R_(0)>1,the existence of at least one locally asymptotically stable endemic equilibrium is shown.Sensitivity analysis of the model,using the parameters relevant to the transmission dynamics of the melioidosis disease,is discussed.Numerical experiments are presented to support the theoretical analysis of the model.In the numerical experimentations,it has been observed that screening and treating individuals in the exposed class has a significant impact on the disease dynamics.
文摘Malaria infection continues to be a major problem in many parts of the world including Africa.Environmental variables are known to significantly affect the population dynamics and abundance of insects,major catalysts of vector-borne diseases,but the exact extent and consequences of this sensitivity are not yet well established.To assess the impact of the variability in temperature and rainfall on the transmission dynamics of malaria in a population,we propose a model consisting of a system of non-autonomous deterministic equations that incorporate the effect of both temperature and rainfall to the dispersion and mortality rate of adult mosquitoes.The model has been validated using epidemiological data collected from the western region of Ethiopia by considering the trends for the cases of malaria and the climate variation in the region.Further,a mathematical analysis is performed to assess the impact of temperature and rainfall change on the transmission dynamics of the model.The periodic variation of seasonal variables as well as the non-periodic variation due to the long-term climate variation have been incorporated and analyzed.In both periodic and non-periodic cases,it has been shown that the disease-free solution of the model is globally asymptotically stable when the basic reproduction ratio is less than unity in the periodic system and when the threshold function is less than unity in the non-periodic system.The disease is uniformly persistent when the basic reproduction ratio is greater than unity in the periodic system and when the threshold function is greater than unity in the non-periodic system.
