Nonstandard finite difference method revisited and application to the Ebola virus disease transmission dynamics

2020 ◽  
Vol 26 (6) ◽  
pp. 818-854 ◽  
Author(s):  
R. Anguelov ◽  
T. Berge ◽  
M. Chapwanya ◽  
J.K. Djoko ◽  
P. Kama ◽  
...  
2021 ◽  
Author(s):  
M.L. Juga ◽  
F. Nyabadza ◽  
F. Chirove

ABSTRACTRecent Ebola virus disease (EVD) outbreaks have been limited not only to the interactions between humans but also to the complex interplay of the environment, human and socio-economic factors. Changes in human behaviour as a result of fear can also affect disease transmission dynamics. In this paper, a compartmental model is used to study the dynamics of EVD incorporating fear and environmental transmission. We formulate a fear dependent contact rate function to measure the rate of person to person, as well as pathogen to person transmissions. The epidemic threshold and the model equilibria are determined and, their stabilities are analysed. The model is validated by fitting it to data from the 2019 and 2020 EVD outbreaks in the Democratic Republic of Congo. Our results suggest that the fear of death from EVD may reduce the transmission and aid the control of the disease, but it is not sufficient to eradicate the disease. Policymakers need to also implement other control measures such as case finding, media campaigns, Quarantine and increase in the number of beds in the Ebola treatment centers, good laboratory services, safe burials and social mobilisation, to eradicate the disease.HighlightsDue to its high case fatality rate, EVD undoubtedly instills fear in the inhabitants of any affected community.We propose an Ebola model with fear, which considers the pathogens in the environment to quantify the effect of fear and environmental transmission on the EVD disease dynamics.The fear of death from Ebola is proportional to the Ebola disease transmission rate.At high levels of fear, the number of EVD cases decrease.


SAINTIFIK ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 15-20
Author(s):  
Darmawati Darmawati

In this paper, mathematical model of measles transmission dynamics considering vaccination and herd immunity is discussed. The solution of the model is investigated using euler, atangana, dan nonstandard finite difference method. After comparing the solutions of the model, we observe that the solutions obtained by using euler and atangana method diverge for certain step. On the other hand, the solutions obtained by using nonstandard finite difference always converge.


2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.


2017 ◽  
Vol 10 (04) ◽  
pp. 1750057 ◽  
Author(s):  
Mudassar Imran ◽  
Adnan Khan ◽  
Ali R. Ansari ◽  
Syed Touqeer Hussain Shah

Ebola virus disease (EVD) has emerged as a rapidly spreading potentially fatal disease. Several studies have been performed recently to investigate the dynamics of EVD. In this paper, we study the transmission dynamics of EVD by formulating an SEIR-type transmission model that includes isolated individuals as well as dead individuals that are not yet buried. Dynamical systems analysis of the model is performed, and it is consequently shown that the disease-free steady state is globally asymptotically stable when the basic reproduction number, [Formula: see text] is less than unity. It is also shown that there exists a unique endemic equilibrium when [Formula: see text]. Using optimal control theory, we propose control strategies, which will help to eliminate the Ebola disease. We use data fitting on models, with and without isolation, to estimate the basic reproductive numbers for the 2014 outbreak of EVD in Liberia and Sierra Leone.


2003 ◽  
Vol 45 (2) ◽  
pp. 181-193 ◽  
Author(s):  
S. M. Moghadas ◽  
A. B. Gumel

AbstractA five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.


2016 ◽  
Vol 113 (16) ◽  
pp. 4488-4493 ◽  
Author(s):  
Li-Qun Fang ◽  
Yang Yang ◽  
Jia-Fu Jiang ◽  
Hong-Wu Yao ◽  
David Kargbo ◽  
...  

Sierra Leone is the most severely affected country by an unprecedented outbreak of Ebola virus disease (EVD) in West Africa. Although successfully contained, the transmission dynamics of EVD and the impact of interventions in the country remain unclear. We established a database of confirmed and suspected EVD cases from May 2014 to September 2015 in Sierra Leone and mapped the spatiotemporal distribution of cases at the chiefdom level. A Poisson transmission model revealed that the transmissibility at the chiefdom level, estimated as the average number of secondary infections caused by a patient per week, was reduced by 43% [95% confidence interval (CI): 30%, 52%] after October 2014, when the strategic plan of the United Nations Mission for Emergency Ebola Response was initiated, and by 65% (95% CI: 57%, 71%) after the end of December 2014, when 100% case isolation and safe burials were essentially achieved, both compared with before October 2014. Population density, proximity to Ebola treatment centers, cropland coverage, and atmospheric temperature were associated with EVD transmission. The household secondary attack rate (SAR) was estimated to be 0.059 (95% CI: 0.050, 0.070) for the overall outbreak. The household SAR was reduced by 82%, from 0.093 to 0.017, after the nationwide campaign to achieve 100% case isolation and safe burials had been conducted. This study provides a complete overview of the transmission dynamics of the 2014−2015 EVD outbreak in Sierra Leone at both chiefdom and household levels. The interventions implemented in Sierra Leone seem effective in containing the epidemic, particularly in interrupting household transmission.


Sign in / Sign up

Export Citation Format

Share Document