Brucellosis is a zoonotic infection caused by Gram-negative bacteria of genus Brucella. The 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. The necessary conditions for an optimal control problem are rigorously analyzed using Pontryagin’s maximum principle. The 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.
Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the formulated model is established using the Box Invariance method, the effective reproduction number, R e of the model is computed using the standard next generation approach. We prove that the brucellosis free equilibrium exists, locally and globally asymptotically stable if R e < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if R e > 1. Sensitivity analysis of the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission rate, vaccination rate, and disease induced culling rate are the most sensitive parameters and should be targeted in designing of the control strategies for the disease. Numerical simulation is done to show the variations of each subpopulation with respect to the control parameters.
A modeling approach to investigate the dynamics of COVID-19 epidemics coupled with fear is presented in this paper. The basic reproduction number
R
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is computed and employed in analysing the effect of initial transmission and the conditions for disease control or eradication. Numerical simulations show that whenever there is an outbreak coupled with fear, the disease is likely to persist in the first two months, and after that, it will start to slow down as the recovery rate from fear increases. An increase in the number of recovered individuals lead to a rise in the number of susceptibles and consequently set off a second wave of infection in the third month of the epidemic.
A deterministic mathematical model for brucellosis that incorporates seasonality on direct and indirect transmission parameters for domestic ruminants, wild animals, humans, and the environment was formulated and analyzed in this paper. Both analytical and numerical simulations are presented. From this study, the findings show that variations in seasonal weather have the great impact on the transmission dynamics of brucellosis in humans, livestock, and wild animals. Thus, in order for the disease to be controlled or eliminated, measures should be timely implemented upon the fluctuation in the transmission of the disease.
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