Analysis of a rabies transmission model with population dispersal (original) (raw)
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Analysis of Rabies in China: Transmission Dynamics and Control
PLoS ONE, 2011
Human rabies is one of the major public-health problems in China. The number of human rabies cases has increased dramatically in the last 15 years, partially due to the poor understanding of the transmission dynamics of rabies and the lack of effective control measures of the disease. In this article, in order to explore effective control and prevention measures we propose a deterministic model to study the transmission dynamics of rabies in China. The model consists of susceptible, exposed, infectious, and recovered subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The model simulations agree with the human rabies data reported by the Chinese Ministry of Health. We estimate that the basic reproduction number R 0~2 for the rabies transmission in China and predict that the number of the human rabies is decreasing but may reach another peak around 2030. We also perform some sensitivity analysis of R 0 in terms of the model parameters and compare the effects of culling and immunization of dogs. Our study demonstrates that (i) reducing dog birth rate and increasing dog immunization coverage rate are the most effective methods for controlling rabies in China; and (ii) large scale culling of susceptible dogs can be replaced by immunization of them.
Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis
Applied and Computational Mathematics, 2015
In this paper we formulate a deterministic mathematical model for the transmission dynamics of rabies in human and animal within and around Addis Ababa, Ethiopia. Our model involves vaccination program for dog population. The basic reproduction number and effective reproduction numbers are computed and the results are entirely depending on the parameters of dog population, which shows the responsibility of dog population for human and livestock infection. For a specified set of values of parameters as deduced from the data provided by Ethiopian Public Health Institute of Addis Ababa, the basic reproduction number 0 R and the effective reproduction number e R works out to be 2 and 1.6 respectively, which indicates the disease will be endemic. The numerical simulation of reproduction ratio shows that the combination of vaccination, culling of stray dogs and controlling annual crop of new born puppies are the best method to control rabies transmission within and around Adds Ababa. The disease-free equilibrium 0 ε is computed. When the effective reproduction number 1 e R < it is proved to be globally asymptotically stable in the feasible region Φ. When 1 e R > there exists one endemic equilibrium point which is locally asymptotically stable.
Population Dynamics of Dogs Subjected To Rabies Disease
2016
In this paper we have considered the population dynamics of dogs subjected to rabies disease. A new mathematical model SEIPIFR is presented which is designed and developed with some reasonable modifications to the corresponding epidemic SEIR model. Disease spread controlling technique called vaccination is included in the present model and studied its impact. Vaccine can be given to both susceptible and exposed individuals so as to control the spread of epidemic. The basic reproduction number is derived using the next generation matrix method. Disease free equilibrium point is found and endemic equilibrium state is identified. It is shown that the disease free equilibrium point is locally and globally asymptotically stable if the reproduction number takes a value less than one unit and unstable if it is more than one unit. Numerical simulation study is conducted using ode45 of MATLAB. The results and interpretations are elaborated and included in the text.
Journal of Advances in Mathematics and Computer Science
Rabies is a zoonotic viral disease that aects all mammals including human beings. Dogs are responsible for 99% of human rabies cases and the disease is always fatal once the symptoms appear. In Kenya the disease is still endemic despite the fact that there are ecient vaccines for controlling the disease. In this project, we developed SIRS mathematical model using a system of ordinary dierential equations from the model to study the transmission dynamics of rabies virusin dogs using public health education as a control strategy. The reproduction number R0 was calculated using the Next Generation Matrix. Both disease free and endemics equilibrium points were determined and their stability analysis performed. From the stability analysis results it was found out that the disease free equilibrium point is both locally and globally asymptotically stable when R0 < 1 and the endemic equilibrium point is both locally and globally asymptotically stable when R0 > 1. Numerical simulations...
Desirable Dog-Rabies Control Methods in an Urban setting in Africa -a Mathematical Model
International Journal of Mathematical Sciences and Computing, 2020
Rabies is a fatal, zoonotic, viral disease that causes an acute inflammation of the brain in humans and other mammals. It is transmitted through contact with bodily fluids of infected mammals, usually via bites or scratches. In this paper, we formulate a deterministic model which measures the effects of different rabies control methods (mass-culling and vaccination of dogs) for urban areas near wildlife, using the Arusha region in Tanzania as an example. Values for various parameters were deduced from five years' worth of survey data on Arusha's dog population. Data included vaccination coverage, dog bites and rabies deaths recorded by a local non-governmental organization and the Ministry of Agriculture, Livestock Development and Fisheries of the United Republic of Tanzania. The basic reproduction number R 0 and effective reproduction number R e were computed and found to be 1.9 and 1.2 respectively. These imply that the disease is endemic in Arusha. The numerical simulation of the reproduction number shows that vaccination is the most appropriate control method for rabies transmission in urban areas near wildlife reservoirs. The disease free equilibrium ε 0 is also computed. If the effective reproduction number R e is computed and found to be less than 1, it implies that it is globally asymptotically stable in the feasible region Φ. If R e > 1 it is implied that there is one equilibrium point which is endemic and it is locally asymptotically stable.
Stability analysis of rabies model with vaccination effect and culling in dogs
Applied Mathematical Sciences, 2015
This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs -domestic dogs -human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh Hurwitz test to analyze the stability of the Disease Free Equilibrium and Endemic Equilibrium of this model.
Modelling the factors affecting the probability for local rabies elimination by strategic control
PLOS Neglected Tropical Diseases, 2021
Dog rabies has been recognized from ancient times and remains widespread across the developing world with an estimated 59,000 people dying annually from the disease. In 2011 a tri-partite alliance consisting of the OIE, the WHO and the FAO committed to globally eliminating dog-mediated human rabies by 2030. Regardless of global support, the responsibility remains with local program managers to implement successful elimination programs. It is well known that vaccination programs have a high probability of successful elimination if they achieve a population-coverage of 70%. It is often quoted that reducing population turnover (typically through sterilizations) raises the probability for local elimination by maintaining herd immunity for longer. Besides this, other factors that affect rabies elimination are rarely mentioned. This paper investigates the probability for local elimination as it relates to immunity, fecundity, dog population size, infectivity (bite rates), in-migration of ...
A Saturated Treatment Model for the Transmission Dynamics of Rabies
Malaysian Journal of Computing,, 2019
Rabies is a viral disease that claims about 59 000 lives globally every year. The ignorance of the fact that man can be a carrier of the disease makes every practical and theoretical approach towards the study of the disease a good development. In this work, a mathematical model is designed to incorporate a saturated incidence rate such that the incidence rate is saturated around the infectious agents. The model is studied qualitatively via stability theory of nonlinear differential equations to assess the effects of general awareness, constant vaccination and the saturated treatment on the transmission dynamics of rabies disease. The effective reproduction number is derived and the numerical simulation is carried out to verify the analytical results. It is discovered that while general awareness plays pivotal roles in averting rabies death, multiple control measures have the tendency of driving rabies to extinction
Mathematical Analysis of Rabies Transmission Dynamics and Control
Journal of Nepal Mathematical Society
Rabies is a dangerous disease that kills many people than any other communicable disease and yet it is underrated. This results from the little knowledge on the myriad ways of transmission of the virus. A deterministic model is proposed to study the spread of the rabies virus in both domestic dogs (Canis familiaries) and humans (Homo sapiens). We elaborately studied the spread of the rabies virus from dogs to-dogs, dogs-to-humans and for the first time, humans-to-humans. Sensitivity analysis is performed to determine the influence of various parameters on the transmission of rabies the most. The rabies-free equilibrium and the endemic equilibrium points were determined and the conditions under which the equilibria are stable were also obtained. The stability conditions provide the conditions under which the disease will persist or get to be eradicated. Numerical solutions of the model were obtained using the ode45 routine in MATLAB. The study demonstrated that for rabies to be eradi...