Skip to content
Research Article Open access CC BY 4.0

Dynamics and Analysis of Chronic Brucellosis in Sheep

Paride O. Lolika, Mlyashimbi Helikumi

Journal of Advances in Mathematics and Computer Science · pp. 61–81 · Published 30 Aug 2022

10.9734/jamcs/2022/v37i730466

Abstract

We proposed and studied a new fractional-order model for the transmission dynamics of brucellosis with a special focus on the sheep-to-sheep transmission. Two control strategies namely; culling and vaccination rate are incorporated in the model. We computed the basic reproduction number R0 and we studied the global stability of disease-free and endemic equilibrium point in terms of basic reproduction number R0: We found that both the disease-free and endemic equilibrium points are globally stable whenever R0 < 1 and R0 > 1 respectively. In numerical simulations, we performed the sensitivity analysis of the model and expressed the relationship between model parameters and R0:We noted that, increase on the magnitude of model parameters with negative correlation coefficients would significantly reduce the spread of Brucellosis disease in the population. Moreover, model validation and parameter estimation for fractional-order and classical integer-order derivatives was carried out using real brucellosis for Egypt, 1999-2011. Overall, we noted that fractional-order model gave better prediction of brucellosis compared to classical integer-order model. Furthermore, we investigated the role of memory effects on the transmission of brucellosis in the population. We observe that, the memory effects have influenceon the transmission of brucellosis in the community. In addition, we noted that the aforementioned control strategies have the potential to reduce the transmission of brucellosis in the population. In particular, we observed that whenever the culling and vaccination rate is greater than 40% and 50% respectively, the disease dies out in the population.

Brucellosis fractional-order model global stability sensitivity analysis parameter estimation

References (37)

  1. 1 A Simplex Method for Function Minimization [DOI]
  2. 2 The Stability of Dynamical Systems [DOI]
  3. 3 Springer Science and Business Media
  4. 4 The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type [DOI]
  5. 5 Brucellosis in humans and animals.
  6. 6 Volterra-type Lyapunov functions for fractional-order epidemic systems [DOI]
  7. 7 Economics of brucellosis impact and control in low-income countries [DOI]
  8. 8 Human brucellosis: an overview [DOI]
  9. 9 Epidemiology of brucellosis in domestic animals caused by Brucella melitensis, Brucella suis and Brucella abortus [DOI]
  10. 10 Control and Eradication of Brucella melitensis Infection in Sheep and Goats [DOI]
  11. 11 The memory effect on fractional calculus: an application in the spread of COVID-19 [DOI]
  12. 12 Global dynamics of an SEIR epidemic model with saturating contact rate [DOI]
  13. 13 Clinical Manifestations of Brucellosis in Domestic Animals and Humans [DOI]
  14. 14 Analysis for fractional dynamics of Ebola virus model [DOI]
  15. 15 Transmission dynamics of brucellosis: Mathematical modelling and applications in China [DOI]
  16. 16 Animal brucellosis in Egypt [DOI]
  17. 17 Prediction and Control of Brucellosis Transmission of Dairy Cattle in Zhejiang Province, China [DOI]
  18. 18 Modelling Seasonal Brucellosis Epidemics in Bayingolin Mongol Autonomous Prefecture of Xinjiang, China, 2010–2014 [DOI]
  19. 19 Model-Based Evaluation of Strategies to Control Brucellosis in China [DOI]
  20. 20 Epidemiological and Clinical Features of Brucellosis in the Country of Georgia [DOI]
  21. 21 Modeling sheep brucellosis transmission with a multi-stage model in Changling County of Jilin Province, China [DOI]
  22. 22 Transmission Dynamics of Fractional Order Brucellosis Model Using Caputo–Fabrizio Operator [DOI]
  23. 23 Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis [DOI]
  24. 24 Transmission dynamics of brucellosis with patch model: Shanxi and Hebei Provinces as cases [DOI]
  25. 25 Global Dynamics of Fractional-order Model for Malaria Disease Transmission [DOI]
  26. 26 Transmission of Brucella melitensis from sheep to lambs [DOI]
  27. 27 On the Role of Short-Term Animal Movements on the Persistence of Brucellosis [DOI]
  28. 28 A Mathematical Model of the Transmission Dynamics and Control of Bovine Brucellosis in Cattle [DOI]
  29. 29 A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity [DOI]
  30. 30 Implications of seasonal variations, host and vector migration on spatial spread of sleeping sickness: Insights from a mathematical model [DOI]
  31. 31 Human brucellosis in the Emirate of Abu Dhabi, United Arab Emirates, 2010–2015 [DOI]
  32. 32 A fractional-order Trypanosoma brucei rhodesiense model with vector saturation and temperature dependent parameters [DOI]
  33. 33 A note on fractional-order model for cholera disease transmission with control strategies [DOI]
  34. 34 Modeling Co-infection of Bovine Brucellosis and Tuberculosis [DOI]
  35. 35 Dynamics of a Reaction Diusion Brucellosis Model [DOI]
  36. 36 International Journal of Environmental Research and Public Health [DOI]
  37. 37 The Memory Effect on Fractional Calculus: An Application in the Spread of Covid-19 [DOI]

Cited by 5

Fractional Optimal Control Strategies for Combating Interspecies Transmission of Brucellosis Based on Real Data from Inner Mongolia

Dilara Yapışkan, B. B. İskender Eroğlu · Iranian Journal of Science · 2026

Analysis of a fractional order Bovine Brucellosis disease model with discrete generalized Mittag–Leffler kernels

M. Farman, A. Shehzad, A. Akgül · Results in Physics · 2023

Fractional-order brucellosis transmission model between interspecies with a saturated incidence rate

Dilara Yapışkan, Beyza Billur İskender Eroğlu · Bulletin of Biomathematics · 2024

Showing 3 of 5 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

36

Page views

0

PDF downloads

4

Outbound clicks

5

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.