Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number $R_{0}$ R 0 of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition $R_{0}<1$ R 0 < 1 . Moreover, we derive the global stability at the disease-free equilibrium point by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, we show the local and global stability to be held under specific conditions and $R_{0}>1$ R 0 > 1 . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

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“…Using the next generation matrix approach [23,24], the Jacobian matrix J for this system at the disease-free equilibrium point is given by…”

Section: Basic Reproductive Number Rmentioning

confidence: 99%

Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

et al. 2021

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“…Thus, under certain conditions (for instance only individuals in the S(t) class can get infected) R t = R 0 S(t)/N, which relates the value of the virus transmissibility β to the effective reproduction number (for more details see [31,78,79]). In addition, in this section we study the global stability of these equilibrium points using some suitable Lyapunov functionals [43,[80][81][82][83][84][85].…”

Section: Mathematical Stability Analysismentioning

confidence: 99%

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

González-Parra

Arenas

2021

Mathematics

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Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

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“…One of the important ideas is to study the spread of COVID-19 through mathematical models. To that end, a number of mathematical models have been developed over the past two years to study local infections, estimate peaks in the number of people infected, and suggest ways to control the spread of the disease [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] .…”

Section: Introductionmentioning

confidence: 99%

Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination

Guo

2022

Chaos, Solitons & Fractals

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As people around the world work to stop the COVID-19 pandemic, mutated COVID-19 (Delta strain) that are more contagious are emerging in many places. How to develop effective and reasonable plans to prevent the spread of mutated COVID-19 is an important issue. In order to simulate the transmission of mutated COVID-19 (Delta strain) in China with a certain proportion of vaccination, we selected the epidemic situation in Jiangsu Province as a case study. To solve this problem, we develop a novel epidemic model with a vaccinated population. The basic properties of the model is analyzed, and the expression of the basic reproduction number is obtained. We collect data on the Delta strain epidemic in Jiangsu Province, China from July 20 to August 5, 2021. The weighted nonlinear least square estimation method is used to fit the daily asymptomatic infected people, common infected people and severe infected people. The estimated parameter values are obtained, the approximate values of the basic reproduction number are calculated . Through the global sensitivity analysis, we identify some parameters that have a greater impact on the prevalence of the disease. Finally, according to the evaluation results of parameter influence, we consider three control measures (vaccination, isolation and nucleic acid testing) to control the spread of the disease. The results of the study found that the optimal control measure is to dynamically adjust the three control measures to achieve the lowest number of infections at the lowest cost. The research in this paper can not only enrich theoretical research on the transmission of COVID-19, but also provide reliable control suggestions for countries and regions experiencing mutated COVID-19 epidemics.

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Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

Cited by 54 publications

References 30 publications

Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

Nonlinear Dynamics of the Introduction of a New SARS-CoV-2 Variant with Different Infectiousness

Modeling and optimal control of mutated COVID-19 (Delta strain) with imperfect vaccination

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