A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of t...A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of the dynamics of Ebola virus disease,here,the infected class is supposed to be divided into subclasses,viz.primary and secondary infected.The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation.The obtained results,qualitatively and quantitatively,suggest that migration and contact rates play an important role in controlling the spreading of disease.Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values,it leads to delay in the stabilization of the system.It is also found that primary reproductive number increases with increase in migration rate.Besides this,the approximate time required to attain stability of the disease model system is also determined.The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.展开更多
Human emotions are considered to be contagious that can be transmitted from one person to another during social interactions.However,interaction with people having excessive negative emotions may make other people d...Human emotions are considered to be contagious that can be transmitted from one person to another during social interactions.However,interaction with people having excessive negative emotions may make other people depressed.Taking this aspect into consideration,a SIR nonlinear model is formulated to investigate the transmission dynamics of depression in social connections.Through qualitative analysis of the model,critical value of depression is determined.Two equilibria,viz.depression free and depression state,are obtained and their stability behaviors are analyzed.The stability analysis reveals the fact that both the equilibria are locally and globally stable,depending on critical value of depression.The sensitivity analysis of crucial parameters of critical value of depression is performed to point out the key parameters that can drastically influence the propagation of depression.The results demonstrate the importance of counselling for depressed persons in order to suppress the growth of depression in social connections.The model calibration has been done for the annual depression cases of Zimbabwe.The results of our study show that individuals will catch major depression disorders more quickly once they get initially(primary)depressed.For this,counselling rate for primary depressed population should be increased.展开更多
文摘A nonlinear SEIR mathematical model is developed to investigate the impact of migrated population,infected with Ebola virus,on human-to-human transmission of Ebola Virus Disease(EVD)in a disease-free area.In view of the dynamics of Ebola virus disease,here,the infected class is supposed to be divided into subclasses,viz.primary and secondary infected.The proposed model is analyzed qualitatively using the stability theory of differential equations and quantitatively using numerical simulation.The obtained results,qualitatively and quantitatively,suggest that migration and contact rates play an important role in controlling the spreading of disease.Critical values for migration and contact rates are evaluated and it is revealed that if these rates go beyond their critical values,it leads to delay in the stabilization of the system.It is also found that primary reproductive number increases with increase in migration rate.Besides this,the approximate time required to attain stability of the disease model system is also determined.The model analysis recommends quarantining the noninfected from the secondary infected in order to control the spreading out of disease.
文摘Human emotions are considered to be contagious that can be transmitted from one person to another during social interactions.However,interaction with people having excessive negative emotions may make other people depressed.Taking this aspect into consideration,a SIR nonlinear model is formulated to investigate the transmission dynamics of depression in social connections.Through qualitative analysis of the model,critical value of depression is determined.Two equilibria,viz.depression free and depression state,are obtained and their stability behaviors are analyzed.The stability analysis reveals the fact that both the equilibria are locally and globally stable,depending on critical value of depression.The sensitivity analysis of crucial parameters of critical value of depression is performed to point out the key parameters that can drastically influence the propagation of depression.The results demonstrate the importance of counselling for depressed persons in order to suppress the growth of depression in social connections.The model calibration has been done for the annual depression cases of Zimbabwe.The results of our study show that individuals will catch major depression disorders more quickly once they get initially(primary)depressed.For this,counselling rate for primary depressed population should be increased.
