Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenge...Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenges due to a changing climate, particularly in regions where the disease is endemic. This disease is significantly impacted by changes in climate, especially rising temperatures and fluctuating rainfall patterns. This study explores the influence of temperature and rainfall abundance on malaria transmission dynamics within the context of Burundi. We have constructed a deterministic model that integrates these climatic parameters into the dynamics of the human host-mosquito vector system. The model’s steady states and basic reproduction number, calculated using the next-generation method, reveal important insights. Numerical simulations demonstrate that both temperature and rainfall significantly influence mosquito population dynamics, leading to distinct effects on malaria transmission. Specifically, we observe that temperatures between 20˚C and 32˚C, along with rainfall ranging from 10 to 30 mm per month, create optimal conditions for mosquito development, thus driving malaria transmission in Burundi. Furthermore, our findings indicate a delayed relationship between rainfall and malaria cases. When rainfall peaks in a given month, malaria does not peak immediately but instead shows a lagged response. Similarly, when rainfall decreases, malaria incidence drops after a certain time lag. This same lagged effect is observed when comparing temperature with confirmed malaria cases in Burundi. These findings highlight the urgent need to consider climate factors in malaria control strategies.展开更多
We formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1- 5 years and adults, above 5 years. The susceptibility and infectivity of an...We formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1- 5 years and adults, above 5 years. The susceptibility and infectivity of an individual depend on age class and residence. The large scale system with 6n equations is reduced into a compact form of 3n equations by a change of variables. Then 3n equations are vectorialized using the matrix theory to get a one dimension, compact form of the system, equation in . Using Vidyasagar theorem?[1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.展开更多
We answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stabili...We answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stability depends on the basic reproduction number, Ro?[2]. If Ro ≤1, the disease-free steady solution is globally asymptotically stable and the disease always dies out. If Ro >1, there exists a unique endemic equilibrium which is globally stable and the disease persists. Application is done on data from Western Kenya. The age structure reduces the level of infection and the populations settle to the equilibrium faster than in the model without age structure.展开更多
COVID-19 is a disease caused by the novel coronavirus SARS-CoV-2 that emerged at the end of December 2019 and has since spread globally.In Kenya,the virus was first detected on 13^(th) March 2020.Soon after,the Kenyan...COVID-19 is a disease caused by the novel coronavirus SARS-CoV-2 that emerged at the end of December 2019 and has since spread globally.In Kenya,the virus was first detected on 13^(th) March 2020.Soon after,the Kenyan government implemented non-pharmaceutical interventions(NPIs)to slow the spread of the disease.The pandemic continued to spread and it evolved into several waves over the years despite the discovery of vaccines and treatment.Mathematical models have been developed to help analyse,predict and simulate the dynamics of the pandemic.These models have largely been confined to single waves,without ready extension to multiple waves.In this paper,we develop a mathematical and computational model that can be extended to multiple waves using various concepts.Among these is the application of computational techniques that convert infection curves with negative gradients to those with positive gradients,in the neighbourhood of the change point,namely,where transition occurs from one wave to the next.This effectively generates a new wave.We then introduce a jump mechanism for the susceptible fraction,allowing further computation to align itself with the observed infection curve.To commence the process,we solved the system of governing ordinary differential equations for the period the epidemic spread without intervention and obtained values for the transmission,recovery and death rates that yielded the basic reproduction number,R_(0)=2.76,which is consistent with other related research.We then applied our model to COVID-19 in Kenya and the computation successfully replicated all the waves and also identified the change points located within the months when COVID-19 variants became dominant.The findings strengthen the proposition that the dominant COVID-19 variants were the major drivers of the waves.The techniques can be extended to new strains of COVID-19,influenza and other respiratory viruses.展开更多
文摘Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenges due to a changing climate, particularly in regions where the disease is endemic. This disease is significantly impacted by changes in climate, especially rising temperatures and fluctuating rainfall patterns. This study explores the influence of temperature and rainfall abundance on malaria transmission dynamics within the context of Burundi. We have constructed a deterministic model that integrates these climatic parameters into the dynamics of the human host-mosquito vector system. The model’s steady states and basic reproduction number, calculated using the next-generation method, reveal important insights. Numerical simulations demonstrate that both temperature and rainfall significantly influence mosquito population dynamics, leading to distinct effects on malaria transmission. Specifically, we observe that temperatures between 20˚C and 32˚C, along with rainfall ranging from 10 to 30 mm per month, create optimal conditions for mosquito development, thus driving malaria transmission in Burundi. Furthermore, our findings indicate a delayed relationship between rainfall and malaria cases. When rainfall peaks in a given month, malaria does not peak immediately but instead shows a lagged response. Similarly, when rainfall decreases, malaria incidence drops after a certain time lag. This same lagged effect is observed when comparing temperature with confirmed malaria cases in Burundi. These findings highlight the urgent need to consider climate factors in malaria control strategies.
文摘We formulate an SIS model describing transmission of highland malaria in Western Kenya. The host population is classified as children, age 1- 5 years and adults, above 5 years. The susceptibility and infectivity of an individual depend on age class and residence. The large scale system with 6n equations is reduced into a compact form of 3n equations by a change of variables. Then 3n equations are vectorialized using the matrix theory to get a one dimension, compact form of the system, equation in . Using Vidyasagar theorem?[1], the graph of the reduced system is shown to be strongly connected and the system is a monotone dynamical system. This means that circulation of malaria parasites among the species and among the patches is strongly connected, hence transmission is sustained. We show that for then-dimensional age structured system the positive orthant is positively invariant for all positive values of the variables.
文摘We answer the stability question of the large scale SIS model describing transmission of highland malaria in Western Kenya in a patchy environment, formulated in [1]. There are two equilibrium states and their stability depends on the basic reproduction number, Ro?[2]. If Ro ≤1, the disease-free steady solution is globally asymptotically stable and the disease always dies out. If Ro >1, there exists a unique endemic equilibrium which is globally stable and the disease persists. Application is done on data from Western Kenya. The age structure reduces the level of infection and the populations settle to the equilibrium faster than in the model without age structure.
文摘COVID-19 is a disease caused by the novel coronavirus SARS-CoV-2 that emerged at the end of December 2019 and has since spread globally.In Kenya,the virus was first detected on 13^(th) March 2020.Soon after,the Kenyan government implemented non-pharmaceutical interventions(NPIs)to slow the spread of the disease.The pandemic continued to spread and it evolved into several waves over the years despite the discovery of vaccines and treatment.Mathematical models have been developed to help analyse,predict and simulate the dynamics of the pandemic.These models have largely been confined to single waves,without ready extension to multiple waves.In this paper,we develop a mathematical and computational model that can be extended to multiple waves using various concepts.Among these is the application of computational techniques that convert infection curves with negative gradients to those with positive gradients,in the neighbourhood of the change point,namely,where transition occurs from one wave to the next.This effectively generates a new wave.We then introduce a jump mechanism for the susceptible fraction,allowing further computation to align itself with the observed infection curve.To commence the process,we solved the system of governing ordinary differential equations for the period the epidemic spread without intervention and obtained values for the transmission,recovery and death rates that yielded the basic reproduction number,R_(0)=2.76,which is consistent with other related research.We then applied our model to COVID-19 in Kenya and the computation successfully replicated all the waves and also identified the change points located within the months when COVID-19 variants became dominant.The findings strengthen the proposition that the dominant COVID-19 variants were the major drivers of the waves.The techniques can be extended to new strains of COVID-19,influenza and other respiratory viruses.
