Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries—Validation and Application to the 2014–2015 Ebola Virus Disease Epidemic (original) (raw)
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Mathematical modeling of Ebola epidemics with public health intervention
The 2014/2015 Ebola epidemic in West Africa is the leading ever recorded, and identifying the integrated and applicable dynamics of public health intervention is a key concern, both for current and future epidemics. Moreover, as transmissibility and mortality are supposed to increase as symptoms progress, intervention approaches may depend on individual’s stage of infection. To inspect these issues, we develop SEIIsR mathematical model that study the control mechanism and spread of Ebola epidemic by reducing Is compartment. This work is intensively analysis the sensitive model parameters, disease free equilibrium point locally and globally asymptotically stability, existence of endemic equilibrium point, simulation study and data fitting. A variety of intervention measures exist to prevent and control epidemic diseases. In this study Isolation and contact tracing are proposed. Isolation is an important control strategy for containing Ebola epidemics. The analysis showed that if the most essential epidemiological parameter so called basic reproductive number R0 < 1 then disease free equilibrium point is stable whereas endemic equilibrium point is exist and stable if R0 > 1. The result indicated that early case detection followed by strict isolation could control Ebola outbreak. Tracing close contacts of cases and contacts of exposed health care workers additionally reduces the number of new infected cases. The study emphasizes the significance of early identification and isolation of Ebola cases to reduce the number of people getting infected. According to the numerical solution early identification or Isolated from Exposed is more significance than infected compartment. The best investigation of this study acknowledged that, it is possible to control the outbreak with short period of time by using effective contact tracing and isolation even if the value of R0 > 1. In SEIIsR model the best fit of cumulative infected case in West Africa is computed to follow simulated curve with R0 = 1.3. Further, the study supports the cumulative death cases due to Ebola epidemic is 63% of the infected individuals. Without intervention Ebola epidemic spread is going on where R0 > 1 whereas it is die out where R0 < 1. If we isolate more than 30% of exposed and infected individuals it is possible to reduce and vanish the epidemics spread.
Journal of Biological Systems, 2017
In this paper, we have formulated a compartmental epidemic model with exponentially decaying transmission rates to understand the Ebola transmission dynamics and study the impact of control measures to basic public health. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. We have calculated the basic reproduction number through next generation matrix and investigated the spatial spread of the epidemic via reaction–diffusion modeling. Instead of fitting the model to the observed pattern of spread, we have used previously estimated parameter values and examined the efficacy of predictions of the designed model vis-à-vis the pattern of spread observed in Sierra Leone, West Africa. Further, we conducted a sensitivity analysis to determine the extent to which improvement in predictions is achievable through better parameterization. We performed numerical simulations with and without control measure for the designed model system. A signifi...
Sensitivity Analysis of the Dynamical Spread of Ebola Virus Disease
— The deterministic epidemiological model of (S, E, Iu, Id, R) were studied to gain insight into the dynamical spread of Ebola virus disease. Local and global stability of the model are explored for disease-free and endemic equilibria. Sensitivity analysis is performed on basic reproduction number to check the importance of each parameter on the transmission of Ebola disease. Positivity solution is analyzed for mathematical and epidemiological posedness of the model. Numerical simulation was analyzed by MAPLE 18 software using embedded Runge-Kutta method of order (4) which shows the parameter that has high impact in the spread of the disease spread of Ebola virus disease.
Mathematical Modeling of Ebola Virus Epidemics
International Journal of Mathematics and Statistical Intervention, 2022
In this work a deterministic and stochastic model is developed to investigate the dynamics of Ebola epidemic. The model includes susceptible, exposed, infected, quarantined and removed or recovered individuals. The model used in this work is based on a deterministic model. The Chowel et. al (2015) work on early detection of Ebola is modified by introducing an assumption that the quarantined class is totally successful and cannot infect the susceptible class. The resulting model is transformed into a stochastic model and solved using the Euler Maruyama method. Data generated with the values assigned to the parameters are used for the simulation. We have been able to develop and analyze a model with an effective isolation of infected individuals and its effect to the basic reproductive number is analyzed. In our simulation, the population of infectious individuals is shown over a period. It is seen that the disease will produce an epidemic and after some time, the infected class maintain a uniform increment.
Modeling the transmission dynamics of Ebola virus disease in Liberia
Scientific reports, 2015
Ebola virus disease (EVD) has erupted many times in some zones since it was first found in 1976. The 2014 EVD outbreak in West Africa is the largest ever, which has caused a large number of deaths and the most serious country is Liberia during the outbreak period. Based on the data released by World Health Organization and the actual transmission situations, we investigate the impact of different transmission routes on the EVD outbreak in Liberia and estimate the basic reproduction number R0 = 2.012 in the absence of effective control measures. Through sensitivity and uncertainty analysis, we reveal that the transmission coefficients of suspected and probable cases have stronger correlations on the basic reproduction number. Furthermore, we study the influence of control measures (isolation and safe burial measures) on EVD outbreak. It is found that if combined control measures are taken, the basic reproduction number will be less than one and thus EVD in Liberia may be well contain...
Modeling of the Deaths Due to Ebola Virus Disease Outbreak in Western Africa
International Journal of Statistics in Medical Research, 2015
Problem: The recent 2014 Ebola virus outbreak in Western Africa is the worst in history. It is imperative that appropriate statistical and mathematical models are used to identify risk factors and to monitor the development and spread of the disease. Method: Deaths data due to Ebola virus disease (EVD) in Guinea, Liberia, and Sierra Leone from October 10, 2014 to March 24, 2015 were collected via Situation Reports published by the World Health Organization [1]. Conditional autoregressive (CAR) models were applied to account for the spatial dependency in the countries along with the temporal dimension of the disease. Bayesian change-point models were used to identify key changes in growth and drop time points in the spatial distribution of deaths due to EVD within each country. Country-specific Poisson and negative binomial mixed models of covariate effects were applied to understand the between-country variability in deaths due to EVD. Results: Both CAR models and generalized linear mixed models identified statistically significant covariate effects; however, the CAR models depended on the interval of data analyzed, whereas the mixed models depended on the underlying distribution assumed. Bayesian change-point models identified one significant change-point in the distribution of deaths due to EVD within each country. Practical Application: CAR models, Bayesian change-point models, and generalized linear mixed models demonstrate useful techniques in modeling the incidence of deaths due to EVD.
A Deterministic Mathematical Model for Ebola Virus incorporating the Vector Population
— Most Mathematical model for Ebola virus in the literature had only the human population. This paper is an attempt to incorporate the host population which will give a clearer view of the transmission dynamics of the deadly disease. The disease free and endemic equilibrium of the model were obtained and analyzed for stability,. Key to our analysis is the basic reproductive number 0 R which is the number of secondary infections that one infective individual would create over the duration of the infectious period provided that everyone else is susceptible. We computed a numerical value for 0 R and conducted a sensitivity analysis of its parameters. Our results reveal that quarantine of infected individual's speeds up recovery time.
Migration of infected animals and humans, and mutation are considered as the source of the introduction of new pathogens and strains into a country. In this paper, we formulate a mathematical model of Ebola virus disease dynamics, that describes the introduction of a new strain of ebolavirus, through either mutation or immigration (which can be continuous or impulsive) of infectives. The mathematical analysis of the model shows that when the immigration of infectives is continuous, the new strain invades a country if its invasion reproduction number is greater than one. When the immigration is impulsive, a newly introduced strain is controllable when its reproduction number is less than the ratio of mortality to the population inflow and only locally stable equilibria exist. This ratio is one if the population size is constant. In case of mutation of the resident strain of ebolavirus, the coexistence of the resident and mutated strains is possible if their respective reproduction nu...
A reliable and competitive mathematical analysis of Ebola epidemic model
Advances in Difference Equations
The purpose of this article is to discuss the dynamics of the spread of Ebola virus disease (EVD), a kind of fever commonly known as Ebola hemorrhagic fever. It is rare but severe and is considered to be extremely dangerous. Ebola virus transmits to people through domestic and wild animals, called transmitting agents, and then spreads into the human population through close and direct contact among individuals. To study the dynamics and to illustrate the stability pattern of Ebola virus in human population, we have developed an SEIR type model consisting of coupled nonlinear differential equations. These equations provide a good tool to discuss the mode of impact of Ebola virus on the human population through domestic and wild animals. We first formulate the proposed model and obtain the value of threshold parameter mathcalR0\mathcal{R}_{0}mathcalR0 R 0 for the model. We then determine both the disease-free equilibrium (DFE) and endemic equilibrium (EE) and discuss the stability of the model. We sh...
Determining Important Parameters in Ebola Epidemics
International Journal of Sciences: Basic and Applied Research, 2016
The dynamics of Ebola can best be understood using a mathematical model that determines its dynamics in the community. The model designed in this study explicitly incorporates the latency period, the different transmission compartments, and immigration and emigration effects. The steady states of the system are analysed for existence of equilibria and their stability investigated. From qualitative analysis of the model, it is established that a disease-free equilibrium exists and is stable when When an endemic equilibrium state exists and is stable. Results show further that the model undergoes a hopf bifurcation at the endemic equilibrium and exhibits periodic oscillations. Sensitivity analysis shows that the most effective control measures are increasing hospitalization and reducing transmission rates. The numerical simulations performed demonstrated the theoretical results.