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Yue Z, Mu Y, Yu K. Dynamic analysis of sheep Brucellosis model with environmental infection pathways. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:11688-11712. [PMID: 37501416 DOI: 10.3934/mbe.2023520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
We develop a mathematical model for the transmission of brucellosis in sheep taking into account external inputs, immunity, stage structure and other factors. We find the the basic reproduction number $ R_0 $ in terms of the model parameters, and prove the global stability of the disease-free equilibrium. Then, the existence and global stability of the endemic equilibrium is proven. Finally, sheep data from Yulin, China are employed to fit the model parameters for three different environmental infection exposure conditions. The variability between different models in terms of control measures are analyzed numerically. Results show that the model is sensitive to the control parameters for different environmental infection exposure functions. This means that in practical modeling, the selection of environmental infection exposure functions needs to be properly considered.
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Affiliation(s)
- Zongmin Yue
- Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China
| | - Yuanhua Mu
- Department of Mathematics, Shaanxi University of Science and Technology, Xi'an 710021, China
| | - Kekui Yu
- Yulin Science and Technology Bureau, Yulin 719053, China
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Yin F, Tang X, Liang T, Huang Y, Wu J. External intervention model with direct and indirect propagation behaviors on social media platforms. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:11380-11398. [PMID: 36124595 DOI: 10.3934/mbe.2022530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
A significant distinction between the COVID-19 pandemic and previous pandemics is the significant role of social media platforms in shaping public adherence to non-pharmaceutical interventions and vaccine acceptance. However, with the recurrence of the epidemic, the conflict between epidemic prevention and production recovery has become increasingly prominent on social media. To help design effective communication strategies to guide public opinion, we propose a susceptible-forwarding-immune pseudo-environment (SFI-PE) dynamic model for understanding the environment with direct and indirect propagation behaviors. Then, we introduce a system with external interventions for direct and indirect propagation behaviors, termed the macro-controlled SFI-PE (M-SFI-PE) model. Based on the numerical analyses that were performed using actual data from the Chinese Sina microblogging platform, the data fitting results prove our models' effectiveness. The research grasps the law of the new information propagation paradigm, and our work bridges the gap between reality and theory in information interventions.
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Affiliation(s)
- Fulian Yin
- State Key Laboratory of Media Convergence and Communication, Communication University of China, Beijing 100024, China
- College of Information and Communication Engineering, Communication University of China, Beijing 100024, China
| | - Xinyi Tang
- College of Information and Communication Engineering, Communication University of China, Beijing 100024, China
| | - Tongyu Liang
- College of Information and Communication Engineering, Communication University of China, Beijing 100024, China
| | - Yanjing Huang
- College of Information and Communication Engineering, Communication University of China, Beijing 100024, China
| | - Jianhong Wu
- Fields-CQAM Laboratory of Mathematics for Public Health, Laboratory for Industrial and Applied Mathematics, York University, Toronto M3J1P3, Canada
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Islam MR, Bulut U, Feria-Arroyo TP, Tyshenko MG, Oraby T. Modeling the Impact of Climate Change on Cervid Chronic Wasting Disease in Semi-Arid South Texas. FRONTIERS IN EPIDEMIOLOGY 2022; 2:889280. [PMID: 38455276 PMCID: PMC10910938 DOI: 10.3389/fepid.2022.889280] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 04/01/2022] [Indexed: 03/09/2024]
Abstract
Chronic wasting disease (CWD) is a spongiform encephalopathy disease caused by the transmission of infectious prion agents. CWD is a fatal disease that affects wild and farmed cervids in North America with few cases reported overseas. Social interaction of cervids, feeding practices by wildlife keepers and climate effects on the environmental carrying capacity all can affect CWD transmission in deer. Wildlife deer game hunting is economically important to the semi-arid South Texas region and is affected by climate change. In this paper, we model and investigate the effect of climate change on the spread of CWD using typical climate scenarios. We use a system of impulsive differential equations to depict the transmission of CWD between different age groups and gender of cervids. The carrying capacity and contact rates are assumed to depend on climate. Due to the polygamy of bucks, we use mating rates that depend on the number of bucks and does. We analyze the stability of the model and use simulations to study the effect of harvesting (culling) on eradicating the disease, given the climate of South Texas. We use typical climate change scenarios based on published data and our assumptions. For the climate indicator, we calculated and utilized the Standard Precipitation Evapotranspiration Index (SPEI). We found that climate change might hinder the efforts to reduce and effectively manage CWD as it becomes endemic to South Texas. The model shows the extinction of the deer population from this region is a likely outcome.
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Affiliation(s)
- Md Rafiul Islam
- Department of Mathematics, Iowa State University, Ames, IA, United States
| | - Ummugul Bulut
- Department of Mathematical, Physical, and Engineering Sciences, Texas A&M University-San Antonio, San Antonio, TX, United States
| | | | | | - Tamer Oraby
- School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, Edinburg, TX, United States
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Dhar B, Gupta PK, Sajid M. Solution of a dynamical memory effect COVID-19 infection system with leaky vaccination efficacy by non-singular kernel fractional derivatives. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:4341-4367. [PMID: 35430818 DOI: 10.3934/mbe.2022201] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
In this paper, the recent trends of COVID-19 infection spread have been studied to explore the advantages of leaky vaccination dynamics in SEVR (Susceptible Effected Vaccinated Recovered) compartmental model with the help of Caputo-Fabrizio (CF) and Atangana-Baleanu derivative in the Caputo sense (ABC) non-singular kernel fractional derivative operators with memory effect within the model to show possible long-term approaches of the infection along with limited defensive vaccine efficacy that can be designed numerically over the closed interval ranging from 0 to 1. One of the main goals is to provide a stepping information about the usefulness of the aforementioned non-singular kernel fractional approaches for a lenient case as well as a critical case in COVID-19 infection spread. Another is to investigate the effect of death rate on state variables. The estimation of death rate for state variables with suitable vaccine efficacy has a significant role in the stability of state variables in terms of basic reproduction number that is derived using next generation matrix method, and order of the fractional derivative. For non-integral orders the pandemic modeling sense viz, CF and ABC, has been compared thoroughly. Graphical presentations together with numerical results have proposed that the methodology is powerful and accurate which can provide new speculations for COVID-19 dynamical systems.
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Affiliation(s)
- Biplab Dhar
- Department of Mathematics-SoPS, DIT University, Uttarakhand 248009, India
| | | | - Mohammad Sajid
- Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah 51452, Saudi Arabia
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Islam MR, Peace A, Medina D, Oraby T. Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles. INTERNATIONAL JOURNAL OF ENVIRONMENTAL RESEARCH AND PUBLIC HEALTH 2020; 17:E2014. [PMID: 32197541 PMCID: PMC7142436 DOI: 10.3390/ijerph17062014] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/25/2020] [Revised: 03/06/2020] [Accepted: 03/09/2020] [Indexed: 11/16/2022]
Abstract
In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms.
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Affiliation(s)
- Md Rafiul Islam
- Department of Mathematics and Statistics, Texas Tech University, 2500 Broadway, Lubbock, TX 79409, USA;
| | - Angela Peace
- Department of Mathematics and Statistics, Texas Tech University, 2500 Broadway, Lubbock, TX 79409, USA;
| | - Daniel Medina
- School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Drive, Edinburg, TX 78539, USA; (D.M.); (T.O.)
| | - Tamer Oraby
- School of Mathematical and Statistical Sciences, The University of Texas Rio Grande Valley, 1201 W. University Drive, Edinburg, TX 78539, USA; (D.M.); (T.O.)
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Mejía‐Salazar MF, Waldner CL, Hwang YT, Bollinger TK. Use of environmental sites by mule deer: a proxy for relative risk of chronic wasting disease exposure and transmission. Ecosphere 2018. [DOI: 10.1002/ecs2.2055] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Affiliation(s)
- María Fernanda Mejía‐Salazar
- Department of Veterinary Pathology University of Saskatchewan 52 Campus Drive Saskatoon Saskatchewan S7N 5B4 Canada
| | - Cheryl L. Waldner
- Department of Large Animal Clinical Sciences University of Saskatchewan 52 Campus Drive Saskatoon Saskatchewan S7N 5B4 Canada
| | - Yeen Ten Hwang
- Department of Veterinary Pathology University of Saskatchewan 52 Campus Drive Saskatoon Saskatchewan S7N 5B4 Canada
- Fish and Wildlife Branch Saskatchewan Ministry of Environment Regina Saskatchewan S4S 5W6 Canada
| | - Trent K. Bollinger
- Department of Veterinary Pathology University of Saskatchewan 52 Campus Drive Saskatoon Saskatchewan S7N 5B4 Canada
- Canadian Wildlife Health Cooperative (CWHC) 52 Campus Drive Saskatoon Saskatchewan S7N 5B4 Canada
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Abstract
Chronic wasting disease (CWD) affects cervids and is the only known prion disease readily transmitted among free-ranging wild animal populations in nature. The increasing spread and prevalence of CWD among cervid populations threaten the survival of deer and elk herds in North America, and potentially beyond. This review focuses on prion ecology, specifically that of CWD, and the current understanding of the role that the environment may play in disease propagation. We recount the discovery of CWD, discuss the role of the environment in indirect CWD transmission, and consider potentially relevant environmental reservoirs and vectors. We conclude by discussing how understanding the environmental persistence of CWD lends insight into transmission dynamics and potential management and mitigation strategies.
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Abstract
Infectious disease dynamics are determined, to a great extent, by the social structure of the host. We evaluated sociality, or the tendency to form groups, in Rocky Mountain mule deer (Odocoileus hemionus hemionus) from a chronic wasting disease (CWD) endemic area in Saskatchewan, Canada, to better understand factors that may affect disease transmission. Using group size data collected on 365 radio-collared mule deer (2008–2013), we built a generalized linear mixed model (GLMM) to evaluate whether factors such as CWD status, season, habitat and time of day, predicted group occurrence. Then, we built another GLMM to determine factors associated with group size. Finally, we used 3 measures of group size (typical, mean and median group sizes) to quantify levels of sociality. We found that mule deer showing clinical signs of CWD were less likely to be reported in groups than clinically healthy deer after accounting for time of day, habitat, and month of observation. Mule deer groups were much more likely to occur in February and March than in July. Mixed-sex groups in early gestation were larger than any other group type in any season. Groups were largest and most likely to occur at dawn and dusk, and in open habitats, such as cropland. We discuss the implication of these results with respect to sociobiology and CWD transmission dynamics.
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