Mathematical model for the infectiology of brucellosis with some control strategies (original) (raw)
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A mathematical model for treatment of bovine brucellosis in cattle population
2017
Brucellosis is an infectious bacterial zoonosis of public health and economic significance. In this paper, a mathematical model describing the propagation of bovine brucellosis within cattle population is formulated. Model analysis is carried out to obtain and establish the stability of the equilibrium points. A threshold parameter referred to as the basic reproduction number mathcalR0mathcal{R}_{0}mathcalR0 is calculated and the conditions under which bovine brucellosis can be cleared in the cattle population are established. It is found out that when mathcalR01mathcal{R}_{0} 1mathcalR01. Using Lyapunov function and Poincair'{e}-Bendixson theory, we prove that the disease-free and endemic equilibrium, respectively are globally asymptotic stable. Numerical simulation reveals that control measures should aim at reducing the magnitude of the parameters for contact rate of infectious cattle with the susceptible and recovered cattle, and increasing treatment rate of infected cattle.
A Review of the Mathematical Models for Brucellosis Infectiology and Control Strategies
Journal of Mathematics and Informatics, 2020
Brucellosis is a zoonotic bacterial infection that can be acquired by humans from infected animals' meat, urine, body fluids, aborted materials, unpasteurized milk, and milk products or contaminated environment. Mathematical models for infectious diseases have been used as important tools in providing useful information regarding the transmission and effectiveness of the available control strategies. In this paper, a review of the available compartmental mathematical models for Brucellosis was done. The main purpose was to assess their structure, populations involved, the available control strategies and suitability in predicting the disease incidence and prevalence in different settings. Diversities have been observed in the reviewed mathematical models; some models incorporated seasonal variations in a single animal population, some ignored the contributions of the contaminated environment while others considered the cattle or sheep population only. Most of the models reviewed have not considered the contribution of wild animals in the dynamics of Brucellosis. Some models do not match the real situation in most affected areas like sub-Saharan African region and Asian countries where wild animals, cattle and small ruminants share grazing areas and water points. Thus, to avoid unreliable results, this review reveals the need to affirm and incorporate wild animals, livestock, humans and seasonal weather parameters in the spread of Brucellosis and in planning for its controls.
MATHEMATICAL MODEL FOR BRUCELLOSIS TRANSMISSION DYNAMICS IN LIVESTOCK AND HUMAN POPULATIONS
Communications in Mathematical Biology and Neuroscience, 2020
Brucellosis is a contagious zoonotic infection caused by bacteria of genus brucella which affects humans and animals. The disease is of veterinary importance, public health concern and economic significance in both developed and developing countries. It is transmitted through direct or indirect contact with infected animals or their contaminated products. In this paper we formulate and analyze a deterministic mathematical model for the transmission dynamics of brucellosis. The model formulated incorporates contaminated environment to human , infected livestock to human, and human to human modes of transmission. The impacts of human treatment in controlling the spread of brucellosis in the human population is investigated. Both analytical and numerical solutions reveal that prolonged human treatment has a significant impact in reducing the spread of Brucellosis in human population only while elimination of the disease in domestic ruminants has promising results to both human and ruminants. Thus, brucellosis control strategies should always focus on elimination of the disease in domestic ruminants.
A Mathematical Model of the Transmission Dynamics and Control of Bovine Brucellosis in Cattle
Abstract and Applied Analysis
Brucellosis is one of the most serious diseases that wreaks havoc on the production of livestock. Despite various efforts made to curb the spread of brucellosis, the disease remains a major health concern to both humans and animals. In this work, a deterministic model is developed to investigate the transmission dynamics and control of bovine brucellosis in a herd of cattle. The disease-free equilibrium point of the model is shown to be locally asymptotically stable whenever basic reproduction number R 0 ≤ 1 and unstable if R 0 > 1 . Also, the endemic equilibrium point of the model is shown to be locally asymptotically stable whenever R 0 > 1 and unstable otherwise. Numerical simulations of the model suggest that vaccination is the most efficient single control intervention. Also, the most efficient pair of control interventions is vaccination and culling of seropositive cattle. However, the best way to control bovine brucellosis in cattle is the combination of the three contr...
Optimal Control Strategies for the Infectiology of Brucellosis
International Journal of Mathematics and Mathematical Sciences, 2020
Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. e disease is of public health, veterinary, and economic significance in most of the developed and developing countries. Direct contact between susceptible and infective animals or their contaminated products are the two major routes of the disease transmission. In this paper, we investigate the impacts of controls of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans on the transmission dynamics of Brucellosis. e necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin's maximum principle. e main ambition is to minimize the spread of brucellosis disease in the community as well as the costs of control strategies. Findings showed that the effective use of livestock vaccination, gradual culling through slaughter of seropositive cattle and small ruminants, environmental hygiene and sanitation, and personal protection in humans have a significant impact in minimizing the disease spread in livestock and human populations. Moreover, cost-effectiveness analysis of the controls showed that the combination of livestock vaccination, gradual culling through slaughter, environmental sanitation, and personal protection in humans has high impact and lower cost of prevention.
FUDMA Journal of Sciences (FJS)
Brucellosis is a multifaceted zoonotic infection with vital epidemiological, economic, and global health effect, principally for human and Livestock populations within developing nations. In this paper a dynamic model of livestock-to-human transmission of the disease is developed. Model investigation is carried out to obtain and establish the stability of the equilibrium points. The basic reproduction number ℜ 0 is calculated and the conditions under which brucellosis can be cleared in the both populations are established. Then, optimal control approach to establish the required conditions for the optimality of the disease eradication or control are applied. Public health education for humans and vaccination for susceptible livestock and treatment for infected humans and livestock. Numerical simulations show the dynamics of disease transmission and the effect of the control strategies.
Individual-based modelling and control of bovine brucellosis
Royal Society open science, 2018
We present a theoretical approach to control bovine brucellosis. We have used individual-based modelling, which is a network-type alternative to compartmental models. Our model thus considers heterogeneous populations, and spatial aspects such as migration among herds and control actions described as pulse interventions are also easily implemented. We show that individual-based modelling reproduces the mean field behaviour of an equivalent compartmental model. Details of this process, as well as flowcharts, are provided to facilitate the reproduction of the presented results. We further investigate three numerical examples using real parameters of herds in the São Paulo state of Brazil, in scenarios which explore eradication, continuous and pulsed vaccination and meta-population effects. The obtained results are in good agreement with the expected behaviour of this disease, which ultimately showcases the effectiveness of our theory.
A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity
Mathematics
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...