PC-Based Sensitivity Analysis of the Basic Reproduction Number of Population and Epidemic Models

2020 ◽  
pp. 205-222
Author(s):  
Francesco Florian ◽  
Rossana Vermiglio
Keyword(s):  
Sensitivity Analysis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Epidemic Models ◽  
The Basic Reproduction Number

scholarly journals Rich Dynamics of a Brucellosis Model with Transport

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Juan Liang ◽  
Zhirong Zhao ◽  
Can Li
Keyword(s):  
Numerical Simulation ◽  
Sensitivity Analysis ◽  
Infectious Diseases ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Great Influence ◽  
Stable State ◽  
Initial Values ◽  
Si Model ◽  
The Basic Reproduction Number

Brucellosis is one of the major infectious diseases in China. In this study, we consider an SI model of animal brucellosis with transport. The basic reproduction number ℛ0 is obtained, and the stable state of the equilibria is analyzed. Numerical simulation shows that different initial values have a great influence on results of the model. In addition, the sensitivity analysis of ℛ0 with respect to different parameters is analyzed. The results reveal that the transport has dual effects. Specifically, transport can lead to increase in the number of infected animals; besides, transport can also reduce the number of infected animals in a certain range. The analysis shows that the number of infected animals can be controlled if animals are transported reasonably.

scholarly journals Epidemic management with admissible and robust invariant sets

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0257598
Author(s):  
Willem Esterhuizen ◽  
Jean Lévine ◽  
Stefan Streif
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Intervention Strategies ◽  
Epidemic Models ◽  
Invariant Sets ◽  
Social Distancing ◽  
The Basic Reproduction Number

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.

scholarly journals Mathematical Model Analysis and Simulation of Visceral Leishmaniasis, Kashgar, Xinjiang, 2004–2016

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Yateng Song ◽  
Tailei Zhang ◽  
Hui Li ◽  
Kai Wang ◽  
Xiaobo Lu
Keyword(s):  
Sensitivity Analysis ◽  
Visceral Leishmaniasis ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Parasite Infection ◽  
Parasitic Disease ◽  
Kala Azar ◽  
Si Model ◽  
The Basic Reproduction Number ◽  
Kashgar Prefecture

Visceral leishmaniasis (VL), known as kala-azar, is a serious parasitic disease. After malaria, VL is the second largest parasitic killer. This paper focuses on the VL transmission around sandflies, dogs, and people. Kashgar is located on the southwestern edge of Xinjiang, where kala-azar parasite infection occurs every year. According to the cases reported in the Kashgar Prefecture from 2004 to 2016, we proposed a dynamic model based on these three populations. The SEIR model was established for human population, the SI model was established for sandfly population, and the SI model was established for dog population. We fitted the model to cumulative cases from 2004 to 2016 for the epidemic in Kashgar and predicted that the cumulative incidence of kala-azar in Kashgar would continue to increase, but its growth rate would gradually slow down, which means that the number of cases would gradually decrease every year. We also estimated the basic reproduction number R0 = 1.76 (95% CI: 1.49–1.93). The sensitivity analysis shows that the mutual infection between sandfly and dog contributes the most to the basic reproduction number, while the transmission proportion of sandfly to the susceptible person and the mutual infection between sandfly and dog contribute the most to the number of leishmaniasis human cases. Therefore, according to the sensitivity analysis results, reducing the contact between sandflies and dogs is an effective way to reduce kala-azar.

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