Mathematical model for the infectiology of brucellosis with some control strategies

Abstract

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.

Optimal Control Strategies for the Infectiology of Brucellosis

“…A mathematical model for the transmission dynamics of brucellosis incorporating the time-dependent controls to some parameters is formulated in this section. Some assumptions used in this section are similar to those in [27,28], but the time-dependent parameters u 1 (t), u 2 (t), u 3 (t), and u 4 (t) make the difference between our previous brucellosis works and the current work. e most important reason for taking preventive and control measures on brucellosis is to minimize the prevalence of the disease, and if possible eradicate it from the population.…”

“…at is solutions of model system (1) with nonnegative initial data remain nonnegative for all time t ≥ 0. We apply the approach Cattle Small ruminants Human in [27,28] to the optimal control model (1). Model system (1) can be expressed in the compact form as follows:…”

“…as in [27,28]. Based on the fact that human-to-human transmission is less than within livestock transmission [37][38][39][40][41][42] and that environmental contamination by humans is negligible, the effective reproduction number and basic reproductive number are, respectively, given by…”

“…us, there is a need to assess the current control strategies and their cost effectiveness if we are to control or eradicate the disease. So far, few studies [10,[26][27][28][29][30][31][32][33] have been developed to analyze dynamics and spread of brucellosis in homogeneous/heterogeneous populations. However, none of these studies had considered the mathematical approach for optimal control and cost effectiveness in reducing or eradicating the disease in cattle, small ruminants, and human populations.…”

Assessing the Impact of Optimal Health Education Programs on the Control of Zoonotic Diseases

“…Mathematical modeling, analysis, and simulation for infectious diseases have proved to be an essential guiding tool that could give a sound direction to policymakers and public health administration on how to effectively prevent and control zoonotic diseases. Mathematical modeling of zoonotic diseases has been a particular area of burgeoning interest over the last few years, see the articles [4,[8][9][10][11][12][13][14][15][16]] for a few representative samples. The current study complements many of the earlier published studies by providing a rigorous qualitative analysis of a mathematical model which seeks to understand the impact of educational campaigns in curtailing the spread of zoonotic diseases.…”