Modeling the Dynamics of Rabies Transmission with Vaccination and Stability Analysis (original) (raw)
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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.
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...
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.
2016
Rabies is among the top ten infectious diseases that kill the majority of rural people in Tanzania (Mundi, 2015). A rabies model by Zhang et al. (2011) is modified by incorporating controls: culling of infected dogs and vaccination of susceptible dogs and exposed humans. Analysis of the simple model shows that the rabies free equilibrium points are both locally and globally asymptotically stable when R0 < 1. Results of sensitivity analysis of the basic reproduction number R0, show that the dog’s transmission rate βdd and rabies mortality rate αd are the most sensitive parameters. Therefore in order to reduce the new rabies cases, intervention strategies that will decrease dog’s transmission rates and increase rabies mortality rates should be applied. Using estimated parameter values, simulation is done to the extended model with vaccination and culling. Results suggest that the combination of culling and vaccination is the optimal intervention strategy that should be applied by K...
Dutse Journal of Pure and Applied Sciences (DUJOPAS), Vol. 8 No. 1a March 2022, 2022
Rabies is a viral disease of nervous system that is often transmitted to human beings through the bite or scratch of rabid animals. The uprising of insecurity globally has forced several people to get dogs in their houses. In this paper the mathematical model of rabies transmission and control was formulated by incorporating vaccination class. The Disease Free Equilibrium (DFE) state of the model was obtain and used to compute the basic reproduction number 0 R. Local stability analysis of the DFE was carried out using Jacobian Matrix techniques. The DFE is locally asymptotically stable if
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.
2015
Rabies is one of the neglected tropical diseases that has persisted for centuries in Ethiopia, and it is endemic within and around Addis Ababa. For the purpose of studying the dynamics of the disease we propose a deterministic mathematical model with human, dog and livestock populations and formulated as a system of ordinary differential equations. Basic reproduction number R0 and effective reproduction number Re are computed using next generation operator. Sensitivity analysis of Re shows the natural death rate of dogs , the annual birth rate of dogs νd, dog-to-dog transmission rate βd, and disease induced death rate σd are found to be the most sensitive parameters of Re. According to numerical simulations of our system rabies transmission will increase within and around Addis Ababa, and may peak in 2024 and 2026 in human and livestock populations respectively. Our simulation shows that 25% vaccination coverage in livestock populations will reduce the future infection by half. T...
Analysis of a rabies transmission model with population dispersal
A two-patch SEIRS epidemic model is proposed to study the impact of travel on the spatial spread of dog rabies between patches with different level of disease prevalence. The basic reproduction number of the system is obtained. It is shown that this number characterizes the disease transmission dynamics: if R 0 < 1, there exists only the disease-free equilibrium which is globally asymptotically stable; and if R 0 > 1 then there is a disease endemic equilibrium and the disease persists. Numerical simulations show that, for the parameter values considered, border restriction does not necessarily always have a positive impact on the overall spread of rabies, only when the border control is properly implemented, then it could contribute to stopping the spatial spread of rabies between patches. We compare the efficiency of three strategies for controlling dog rabies: culling, immunization, culling and immunization. Our studies show that dog rabies in China can be controlled by reducing the birth rate of dogs, increasing the immunization rate of dogs.
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...
Modelling of Rabies Transmission Dynamics Using Optimal Control Analysis
Journal of Applied Mathematics, 2017
We examine an optimal way of eradicating rabies transmission from dogs into the human population, using preexposure prophylaxis (vaccination) and postexposure prophylaxis (treatment) due to public education. We obtain the disease-free equilibrium, the endemic equilibrium, the stability, and the sensitivity analysis of the optimal control model. Using the Latin hypercube sampling (LHS), the forward-backward sweep scheme and the fourth-order Range-Kutta numerical method predict that the global alliance for rabies control’s aim of working to eliminate deaths from canine rabies by 2030 is attainable through mass vaccination of susceptible dogs and continuous use of pre- and postexposure prophylaxis in humans.