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Keywords = SEAIS endemic model

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17 pages, 966 KB  
Article
Study on SEAI Model of COVID-19 Based on Asymptomatic Infection
by Lidong Huang, Yue Xia and Wenjie Qin
Axioms 2024, 13(5), 309; https://doi.org/10.3390/axioms13050309 - 8 May 2024
Cited by 3 | Viewed by 2236
Abstract
In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when [...] Read more.
In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number R0 and calculate the equilibrium point. Secondly, when R0<1, the local asymptotic stability of the disease-free equilibrium is proved by Hurwitz criterion, and the global asymptotic stability of the disease-free equilibrium is proved by constructing the Lyapunov function. When R0>1, the system has a unique endemic equilibrium point and is locally asymptotically stable, and it is also proved that the system is uniformly persistent. Then, the application of optimal control theory is carried out, and the expression of the optimal control solution is obtained. Finally, in order to verify the correctness of the theory, the stability of the equilibrium point is numerically simulated and the sensitivity of the parameters of R0 is analyzed. We also simulated the comparison of the number of asymptomatic infected people and symptomatic infected people before and after adopting the optimal control strategy. This shows that the infection of asymptomatic people cannot be underestimated in the spread of COVID-19 virus, and an isolation strategy should be adopted to control the spread speed of the disease. Full article
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19 pages, 3347 KB  
Article
Mathematical Analysis of an Anthroponotic Cutaneous Leishmaniasis Model with Asymptomatic Infection
by Muntaser Safan and Alhanouf Altheyabi
Mathematics 2023, 11(10), 2388; https://doi.org/10.3390/math11102388 - 21 May 2023
Cited by 7 | Viewed by 2424
Abstract
This work aims mainly to study the impact of experiencing asymptomatic anthroponotic cutaneous leishmaniasis (ACL) infection on the overall dynamics and outcomes of the disease. Therefore, a deterministic model for the transmission dynamics of ACL of type SEAIS in the human host and [...] Read more.
This work aims mainly to study the impact of experiencing asymptomatic anthroponotic cutaneous leishmaniasis (ACL) infection on the overall dynamics and outcomes of the disease. Therefore, a deterministic model for the transmission dynamics of ACL of type SEAIS in the human host and SI in sandfly populations is proposed and mathematically analyzed. The model is shown to be well-posed. Its equilibrium and stability analyses are shown. The equilibrium analysis shows that the model has an ACL-free equilibrium that is proven to be locally and globally asymptotically stable if and only if R0<1. In addition, the model has a unique ACL-endemic equilibrium that is shown to exist and be locally asymptotically stable if and only if R0>1. Numerical simulations are performed to show the asymptotic stability of these equilibriums. In addition, the effect of ignoring asymptomatic infections is studied and the analysis shows that ignoring the development of asymptomatic infections overestimates the effort required to eliminate the infection. Moreover, it implies inaccurate measures of controlling ACL infection, especially those based on either using insecticide sprays or bednets. Full article
(This article belongs to the Special Issue Mathematical Methods and Models in Epidemiology)
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