Dynamics and Stability Analysis of a Brucellosis Model with Two Discrete Delays

Lolika, Paride O.; Mushayabasa, Steady

doi:10.1155/2018/6456107

Cited by 14 publications

(5 citation statements)

References 22 publications

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“…Several mathematical models of brucellosis have been developed by researchers. Their authors have used various mathematical approaches: ordinary differential equations with waning of immunity [9][10][11][12][13][14][15][16], culling [17][18][19], treatment and vaccination [18,20], seasonality [21], and partial differential equations with age of infection [22] and seasonality [23]. Ainseba et al [24] proposed an unstructured model to study the transmission of brucellosis.…”

Section: Mathematical Modelmentioning

confidence: 99%

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A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

et al. 2022

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This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number R0 and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Value of parameter µ 0 : Following [17,18], the natural mortality rate in cattle is µ 0 = 0.25 year −1 .…”

Section: Model Parametersmentioning

confidence: 99%

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

et al. 2022

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“…The use of mathematical models plays an important role in studying the transmission dynamics of infectious diseases and is very useful for deciding on the appropriate disease control strategies. Over the past two decades, various mathematical models have been formulated and analyzed to study the dynamics and control of parasitic foodborne diseases such as cholera, brucellosis and echinococcus [6,20,24,28,32,37,38]. In particular, some statistical and deterministic models with some stochastic elements that have been formulated and analyzed to study the transmission dynamics and control of taeniasis and cysticercosis in humans and pigs can be found in Gonzalez et al [12], Kyvsgaard et al [16], Braae et al [2], Winskill et al [34], José et al [14] and Sánchez-Torreset al [27].…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

Mwasunda

Irunde²,

Kajunguri

et al. 2021

Adv Differ Equ

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Taeniasis and cysticercosis pose a significant challenge to food safety and public health. Cysticercosis reduces the market value for pigs and cattle by making pork and beef unsafe for consumption. In this paper, a mathematical model for the transmission dynamics of taeniasis and cysticercosis in humans, pigs and cattle is formulated and analyzed. The analysis shows that both the disease free equilibrium (DFE) and the endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number $R_{0}$ R 0 by next generation matrix method. When $R_{0}< 1$ R 0 < 1 , the DFE is globally asymptotically stable whereas when $R_{0} > 1$ R 0 > 1 the EE is globally asymptotically stable. The normalized forward sensitivity index was used to determine sensitive parameters to the diseases. Humans’ recruitment rate, probability of humans’ infection with taeniasis and the defecation rate of taenia eggs by humans with taeniasis are the most positive sensitive parameters to diseases’ transmission whereas the human natural death rate is the most negative sensitive parameter. However, it is biologically unethical and not practical to increase human natural mortality rate for disease control. In this case, other parameters with negative sensitivity indices such as death rate of taenia eggs and proportions of unconsumed infected beef and pork can be considered for disease control. Generally, to control the diseases, more efforts should be made directed to reducing the number of humans who have taeniasis and defecate in the open environment. Also meat inspection and indoor keeping of cattle and pigs should be emphasized.

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“…Mathematical modeling, analysis and simulation of brucellosis play a crucial role on providing useful insight into the disease dynamics that could guide public health administration for designing effective prevention and control measures. Recently, mathematical modeling of brucellosis dynamics has been an interesting topic for a couple of researchers (see, for example [4,5,6,7,8,9,10,11,12,13]). These studies and several other studies undeniably revealed many useful results and improved the existing knowledge on brucellosis dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Reaction Diusion Brucellosis Model

Lolika

Mushayabasa

2021

JAMCS

Self Cite

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To understand the effects of animal movement on transmission and control of brucellosis infection, a reaction diffusion partial differential equation (PDE) brucellosis model that incorporates wild and domesticated animals under homogeneous Neumann boundary conditions is proposed and analysed. We computed the reproductive number for the brucellosis model in the absence of spatial movement and we established that, the associated model has a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less or equal to unity. However, if the reproductive number is greater than unity an endemic equilibrium point which is globally asymptotically stable exists. We performed sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. For the model with spatial movement the disease threshold is studied by using the basic reproductive number. Additionally we investigate the existence of a Turing stability and travelling waves. Our results shows that incorporating diffusive spatial spread does not produce a Turing instability when the reproductive number R0ODE associated with the ODE model is less than unity. Finally the results suggest that minimizing interaction between buffalo and cattle population can be essential to manage brucellosis spillover between domesticated and wildlife animals. Numerical simulations are carried out to support analytical findings.

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Dynamics and Stability Analysis of a Brucellosis Model with Two Discrete Delays

Cited by 14 publications

References 22 publications

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity

Modeling and analysis of taeniasis and cysticercosis transmission dynamics in humans, pigs and cattle

Dynamics of a Reaction Diusion Brucellosis Model

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