In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international sp...In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.展开更多
Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium parasites.There are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plas...Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium parasites.There are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plasmodium Vivax,are the most dangerous.In Djibouti,the two species of Plasmodium are present in different proportions in the infected population:77%of P.Falciparum and 33%of P.Vivax.In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection.We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model(i.e.,existence and stability of various eqiuilibria).Then we use computational approaches to:(a)identify model parameters using real data on malaria infections in Djibouti;(b)illustrate the influence of different estimated parameters on the basic reproduction numbers;(c)perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans,for infections with each of the Plasmodium species.The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti.In addition,sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates.Finally,the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.展开更多
文摘In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.
基金funded by CEALT(Centre d’Excellence Africain en Logistique et Transport)of the University of DjiboutiCEALT for their financial supportsupport from the MODCOV19 platform of the National Institute of Mathematical Sciences and their Interactions,(CNRS).
文摘Malaria is an infectious and communicable disease,caused by one or more species of Plasmodium parasites.There are five species of parasites responsible for malaria in humans,of which two,Plasmodium Falciparum and Plasmodium Vivax,are the most dangerous.In Djibouti,the two species of Plasmodium are present in different proportions in the infected population:77%of P.Falciparum and 33%of P.Vivax.In this study we present a new mathematical model describing the temporal dynamics of Plasmodium Falciparum and Plasmodium Vivax co-infection.We focus briefly on the well posedness of this model and on the calculation of the basic reproductive numbers for the infections with each Plasmodium species that help us understand the long-term dynamics of this model(i.e.,existence and stability of various eqiuilibria).Then we use computational approaches to:(a)identify model parameters using real data on malaria infections in Djibouti;(b)illustrate the influence of different estimated parameters on the basic reproduction numbers;(c)perform global sensitivity and uncertainty analysis for the impact of various model parameters on the transient dynamics of infectious mosquitoes and infected humans,for infections with each of the Plasmodium species.The originality of this research stems from employing the FAST method and the LHS method to identify the key factors influencing the progression of the disease within the population of Djibouti.In addition,sensitivity analysis identified the most influential parameter for Falciparium and Vivax reproduction rates.Finally,the uncertainty analysis enabled us to understand the variability of certain parameters on the infected compartments.
