Mathematical model for brucellosis transmission dynamics in livestock and human populations

This research article published by Communications in Mathematical Biology and Neuroscience, 2020Brucellosis 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 ruminant

A Review of the Mathematical Models for Brucellosis Infectiology and Control Strategies

This research article published by the Journal of Mathematics and Informatics Vol. 19, 2020Brucellosis 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

Optimal Control Strategies for the Infectiology of Brucellosis

This research article published by Hindawi, 2020Brucellosis 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

Global sensitivity analysis and optimal control of Typhoid fever transmission dynamics

This paper presents a mathematical model aimed at studying the global behaviour and optimal control strategies for Typhoid fever. The primary objective of this study is to identify the most effective control strategy that minimizes the spread of the disease. To achieve this, we calculate the effective and basic reproduction numbers and utilize them to investigate the existence and stability of the equilibria. Furthermore, we investigate the global impact of each model parameter on the variables using Latin Hypercube Sampling and Partial Rank Correlation Coefficient. The necessary conditions of the optimal control problem are analyzed using Pontryagin’s maximum principle, and the numerical values of the model parameters are estimated using the maximum likelihood estimator. The results indicate that the optimal use of vaccination for susceptible individuals, as well as the screening and treatment of asymptomatic infected individuals, have a significant impact on reducing the spread of the disease in endemic regions

Fractional-Order Derivative Model of Rift Valley Fever in Urban Peridomestic Cycle

Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number ℛ0 is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order α=1,0.75,0.5, and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of α decreases. The infected population decreases with a decrease in the value of α. However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for α=1. Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics

Modeling the Dynamics of Coronavirus Disease Pandemic Coupled with Fear Epidemics

A modeling approach to investigate the dynamics of COVID-19 epidemics coupled with fear is presented in this paper. The basic reproduction number R0 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

Modeling the impact of climate change on the dynamics of Rift Valley Fever

A deterministic SEIR model of rift valley fever (RVF) with climate change parameters was considered to compute the basic reproduction number R0 and investigate the impact of temperature and precipitation on R0. To study the effect of model parameters to R0, sensitivity and elasticity analysis of R0 were performed. When temperature and precipitation effects are not considered,R0 is more sensitive to the expected number of infected Aedes spp. due to one infected livestock andmore elastic to the expected number of infected livestock due to one infected Aedes spp.When climatic data are used,R0 is found to bemore sensitive and elastic to the expected number of infected eggs laid by Aedes spp. via transovarial transmission, followed by the expected number of infected livestock due to one infected Aedes spp. and the expected number of infected Aedes spp. due to one infected livestock for both regions Arusha and Dodoma. These results call for attention to parameters regarding incubation period, the adequate contact rate of Aedes spp. and livestock, the infective periods of livestock and Aedes spp., and the vertical transmission in Aedes species.This article is also available at http://dx.doi.org/10.1155/2014/627586TanzaniaMeteorological Agency (TMA),University of Iringa, and Nelson Mandela African Institution of Science and Technology (NM-AIST