There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction between the HIV virions and the CD4+ T-cells. This paper brings...There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction between the HIV virions and the CD4+ T-cells. This paper brings in the intervention of the CD8+ T-cells in seeking, destroying, and killing the infected CD4+ T-cells during early stages of infection. The paper presents and analyses a five-component in-vivo model and applies the results in investigating the in-vivo dynamics of HIV in presence of the CD8+ T-cells. We prove the positivity and the boundedness of the model solutions. In addition, we show that the solutions are biologically meaningful. Both the endemic and virions- free equilibria are determined and their stability investigated. In addition, the basic reproductive number is derived by the next generation matrix method. We prove that the virions-free equilibrium state is locally asymptotically stable if and only if R0 < 1 and unstable otherwise. The results show that at acute infection the CD8+ T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans-critical bifurcation for some set of parameters for R0 . This is a clear indication that having R0 is not sufficient condition for virions depletion.展开更多
The coronavirus disease 2019(COVID-19)pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa.As reported by the World Health Organization,the o...The coronavirus disease 2019(COVID-19)pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa.As reported by the World Health Organization,the outbreak of COVID-19 has spread across the world,killed many,collapsed economies and changed the way people live since it was first reported inWuhan,China,in the end of 2019.As at the end of December 2020,it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths.The trend poses a huge threat to global public health.Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time.The model is concise in structure,and successfully captures the course of the COVID-19 outbreak,and thus sheds light on understanding the trends of the outbreak.The next generation matrix approach was adopted to calculate the basic reproduction number(R_(0))from the model to assess the factors driving the infection.The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change.The results have significant impact on the management of COVID-19 and implementation of prevention policies.The results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.展开更多
This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations.Pontryagin's Maximum Principle is applied to establish optimal control strategies agai...This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations.Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes,infected hepatocytes and malaria parasites.Results from numerical simulation reveal that a combination of preerythrocytic vaccine antigen,blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical P.falciparum malaria.Sensitivity analysis,further reveal that the efficacy of blood schizontocides and blood stage vaccines are crucial in the control of clinical malaria infection.Futhermore,we found that an effective blood schizontocide should be used alongside efficacious blood stage vaccine for rapid eradication of infective malaria parasites.The authors hope that the results of this study will help accelerate malaria elimination efforts by combining malaria vaccines and anti-malarial drugs against the deadly P.falciparum malaria.展开更多
文摘There have been many mathematical models aimed at analysing the in-vivo dynamics of HIV. However, in most cases the attention has been on the interaction between the HIV virions and the CD4+ T-cells. This paper brings in the intervention of the CD8+ T-cells in seeking, destroying, and killing the infected CD4+ T-cells during early stages of infection. The paper presents and analyses a five-component in-vivo model and applies the results in investigating the in-vivo dynamics of HIV in presence of the CD8+ T-cells. We prove the positivity and the boundedness of the model solutions. In addition, we show that the solutions are biologically meaningful. Both the endemic and virions- free equilibria are determined and their stability investigated. In addition, the basic reproductive number is derived by the next generation matrix method. We prove that the virions-free equilibrium state is locally asymptotically stable if and only if R0 < 1 and unstable otherwise. The results show that at acute infection the CD8+ T-cells play a paramount role in reducing HIV viral replication. We also observe that the model exhibits backward and trans-critical bifurcation for some set of parameters for R0 . This is a clear indication that having R0 is not sufficient condition for virions depletion.
文摘The coronavirus disease 2019(COVID-19)pandemic reached Kenya in March 2020 with the initial cases reported in the capital city Nairobi and in the coastal area Mombasa.As reported by the World Health Organization,the outbreak of COVID-19 has spread across the world,killed many,collapsed economies and changed the way people live since it was first reported inWuhan,China,in the end of 2019.As at the end of December 2020,it had led to over 2.8 million confirmed cases in Africa with over 67 thousand deaths.The trend poses a huge threat to global public health.Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas.We employed a SEIHCRD mathematical transmission model with reported Kenyan data on cases of COVID-19 to estimate how transmission varies over time.The model is concise in structure,and successfully captures the course of the COVID-19 outbreak,and thus sheds light on understanding the trends of the outbreak.The next generation matrix approach was adopted to calculate the basic reproduction number(R_(0))from the model to assess the factors driving the infection.The model illustrates the effect of mass testing on COVID-19 as well as individual self initiated behavioral change.The results have significant impact on the management of COVID-19 and implementation of prevention policies.The results from the model analysis shows that aggressive and effective mass testing as well as individual self initiated behaviour change play a big role in getting rid of the COVID-19 epidemic otherwise the rate of infection will continue to increase despite the increased rate of recovery.
文摘This paper presents an in-host malaria model subject to anti-malarial drug treatment and malaria vaccine antigens combinations.Pontryagin's Maximum Principle is applied to establish optimal control strategies against infected erythrocytes,infected hepatocytes and malaria parasites.Results from numerical simulation reveal that a combination of preerythrocytic vaccine antigen,blood schizontocide and gametocytocide drugs would offer the best strategy to eradicate clinical P.falciparum malaria.Sensitivity analysis,further reveal that the efficacy of blood schizontocides and blood stage vaccines are crucial in the control of clinical malaria infection.Futhermore,we found that an effective blood schizontocide should be used alongside efficacious blood stage vaccine for rapid eradication of infective malaria parasites.The authors hope that the results of this study will help accelerate malaria elimination efforts by combining malaria vaccines and anti-malarial drugs against the deadly P.falciparum malaria.
