scholarly journals Effects of Fogging and Mosquito Repellent on the Probability of Disease Extinction for Dengue Fever

2021 ◽  
Vol 4 (1) ◽  
pp. 1-13
Author(s):  
Glenn Lahodny Jr. ◽  
Mona Zevika
Keyword(s):  
Markov Chain ◽  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Markov Chain Model ◽  
Chain Model ◽  
Multitype Branching Process ◽  
The Basic Reproduction Number

A Continuous-Time Markov Chain model is constructed based on the a deterministic model of dengue fever transmission including mosquito fogging and the use of repellent. The basic reproduction number (R0) for the corresponding deterministic model is obtained. This number indicates the possible occurrence of an endemic at the early stages of the infection period. A multitype branching process is used to approximate the Markov chain. The construction of offspring probability generating functions related to the infected states is used to calculate the probability of disease extinction and the probability of an outbreak (P0). Sensitivity analysis is shown for variation of control parameters and for indices of the basic reproduction number. These results allow for a better understanding of the relation of the basic reproduction number with other indicators of disease transmission.

scholarly journals On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
Author(s):  
Malen Etxeberria-Etxaniz ◽  
Santiago Alonso-Quesada ◽  
Manuel De la Sen
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Impulsive Vaccination ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

2015 ◽  
Vol 23 (03) ◽  
pp. 423-455
Author(s):  
P. MOUOFO TCHINDA ◽  
JEAN JULES TEWA ◽  
BOULECHARD MEWOLI ◽  
SAMUEL BOWONG
Keyword(s):  
Drug Therapy ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Time Delays ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Global Dynamics ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

scholarly journals Using a stochastic continuous-time Markov chain model to examine alternative timing and duration of the COVID-19 lockdown in Kuwait: what can be done now?

2022 ◽  
Vol 80 (1) ◽  
Author(s):  
Mustafa Al-Zoughool ◽  
Tamer Oraby ◽  
Harri Vainio ◽  
Janvier Gasana ◽  
Joseph Longenecker ◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Disease Transmission ◽  
Markov Chain Model ◽  
Substantial Reduction ◽  
Control Measures ◽  
Optimal Timing ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Epidemic Curve

Abstract Background Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations. Methods The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and spread of SARS-CoV 2. Transmission of infection occurs between individuals through social contacts at home, in schools, at work, and during other communal activities. Results The model shows that a lockdown 10 days before the epidemic peak for 90 days is optimal but a more realistic duration of 45 days can achieve about a 45% reduction in both new infections and case hospitalizations. Conclusions In the view of the forthcoming waves of the COVID19 pandemic anticipated in Kuwait using a correctly-timed and sufficiently long lockdown represents a workable management strategy that encompasses the most stringent form of social distancing with the ability to significantly reduce transmissions and hospitalizations.

scholarly journals Analysis of the Model on the Effect of Seasonal Factors on Malaria Transmission Dynamics

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Victor Yiga ◽  
Hasifa Nampala ◽  
Julius Tumwiine
Keyword(s):  
Malaria Transmission ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Current Control ◽  
Transmission Dynamics ◽  
Mosquito Vector ◽  
The Impact ◽  
The Basic Reproduction Number

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value θ , defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

scholarly journals COVID-19 disease transmission model considering direct and indirect transmission

2020 ◽  
Vol 202 ◽  
pp. 12008
Author(s):  
Dipo Aldila
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Model ◽  
Indirect Transmission ◽  
Variation Of Parameters ◽  
The Media ◽  
Disease Transmission Model ◽  
The Basic Reproduction Number

A mathematical model for understanding the COVID-19 transmission mechanism proposed in this article considering two important factors: the path of transmission (direct-indirect) and human awareness. Mathematical model constructed using a four-dimensional ordinary differential equation. We find that the Covid-19 free state is locally asymptotically stable if the basic reproduction number is less than one, and unstable otherwise. Unique endemic states occur when the basic reproduction number is larger than one. From sensitivity analysis on the basic reproduction number, we find that the media campaign succeeds in suppressing the endemicity of COVID-19. Some numerical experiments conducted to show the dynamic of our model respect to the variation of parameters value.

scholarly journals The Effect of Seasonal Weather Variation on the Dynamics of the Plague Disease

2017 ◽  
Vol 2017 ◽  
pp. 1-25 ◽  
Author(s):  
Rigobert C. Ngeleja ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Weather Conditions ◽  
Effective Control ◽  
Human Beings ◽  
Weather Variation ◽  
The Basic Reproduction Number ◽  
Seasonal Weather

Plague is a historic disease which is also known to be the most devastating disease that ever occurred in human history, caused by gram-negative bacteria known as Yersinia pestis. The disease is mostly affected by variations of weather conditions as it disturbs the normal behavior of main plague disease transmission agents, namely, human beings, rodents, fleas, and pathogens, in the environment. This in turn changes the way they interact with each other and ultimately leads to a periodic transmission of plague disease. In this paper, we formulate a periodic epidemic model system by incorporating seasonal transmission rate in order to study the effect of seasonal weather variation on the dynamics of plague disease. We compute the basic reproduction number of a proposed model. We then use numerical simulation to illustrate the effect of different weather dependent parameters on the basic reproduction number. We are able to deduce that infection rate, progression rates from primary forms of plague disease to more severe forms of plague disease, and the infectious flea abundance affect, to a large extent, the number of bubonic, septicemic, and pneumonic plague infective agents. We recommend that it is more reasonable to consider these factors that have been shown to have a significant effect on RT for effective control strategies.

scholarly journals Using a Stochastic Continuous-Time Markov Chain Model to Examine Alternative Timing and Duration of the COVID-19 Lockdown in Kuwait: What Can be Done Now?

2021 ◽  
Author(s):  
Mustafa Al-Zoughool ◽  
Tamer Oraby ◽  
Harri Vainio ◽  
Janvier Gasana ◽  
Joseph Longnecker ◽  
...  
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Disease Transmission ◽  
Markov Chain Model ◽  
Substantial Reduction ◽  
Control Measures ◽  
Optimal Timing ◽  
Chain Model ◽  
Continuous Time Markov Chain ◽  
Epidemic Curve

Abstract Background: Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations. Methods: The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and spread of SARS-CoV 2. Transmission of infection occurs between individuals through social contacts at home, in schools, at work, and during other communal activities. Results: The model shows that a lockdown 10 days before the epidemic peak for 90 days is optimal but a more realistic duration of 45 days can achieve about a 45% reduction in both new infections and case hospitalizations.Conclusions: In the view of the forthcoming waves of the COVID19 pandemic anticipated in Kuwait using a correctly-timed and sufficiently long lockdown represents a workable management strategy that encompasses the most stringent form of social distancing with the ability to significantly reduce transmissions and hospitalizations.

scholarly journals Mathematics Model Development Deployment of Dengue Fever Diseases by Involve Human and Vectors Exposed Components

2018 ◽  
Vol 8 (4) ◽  
Author(s):  
Flaviana Priscilla Persulessy ◽  
Paian Siantur ◽  
Jaharuddin .
Keyword(s):  
Dengue Virus ◽  
Equilibrium Point ◽  
Dengue Fever ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Model Development ◽  
Endemic Equilibrium ◽  
Mathematics Model ◽  
Sensitivity Index ◽  
The Basic Reproduction Number

Dengue virus is one of virus that cause deadly disease was dengue fever. This virus was transmitted through bite of Aedes aegypti female mosquitoes that gain virus infected by taking food from infected human blood, then mosquitoes transmited pathogen to susceptible humans. Suppressed the spread and growth of dengue fever was important to avoid and prevent the increase of dengue virus sufferer and casualties. This problem can be solved with studied important factors that affected the spread and equity of disease by sensitivity index. The purpose of this research were to modify mathematical model the spread of dengue fever be SEIRS-ASEI type, to determine of equilibrium point, to determined of basic reproduction number, stability analysis of equilibrium point, calculated sensitivity index, to analyze sensitivity, and to simulate numerical on modification model. Analysis of model obtained disease free equilibrium (DFE) point and endemic equilibrium point. The numerical simulation result had showed that DFE, stable if the basic reproduction number is less than one and endemic equilibrium point was stable if the basic reproduction number is more than one.

Banana Xanthomonas wilt dynamics with mixed cultivars in a periodic environment

2019 ◽  
Vol 13 (01) ◽  
pp. 2050005
Author(s):  
Juliet N. Nakakawa ◽  
Joseph Y. T. Mugisha ◽  
Michael W. Shaw ◽  
Eldad Karamura
Keyword(s):  
Basic Reproduction Number ◽  
Rainy Season ◽  
Autonomous System ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Control Measures ◽  
Disease Dynamics ◽  
Periodic Environment ◽  
The Basic Reproduction Number ◽  
Banana Xanthomonas Wilt

In this paper, we study a deterministic model with non-autonomous system for mixed cultivars to assess the effect of cultivar susceptibility and seasonal variation on banana Xanthomonas wilt (BXW) disease dynamics. A special case of two cultivars classified as highly susceptible for inflorescence infection (ABB) and less susceptible (AAA) cultivar is considered. The basic reproduction number corresponding to the non-autonomous system is derived and numerically computed to determine disease dynamics. Results showed that the disease dies out whenever the periodic basic reproduction number is less than unity and a periodic solution is obtained when it is greater than one. Results further showed that for both cultivars, the basic reproduction number increases with increasing values of the transmission rates and declines exponentially with increasing values of roguing rates. The critical roguing rate of ABB-genome cultivar was higher than that of AAA-genome cultivars. The peaks in disease prevalence indicate the importance of effective implementation of controls during the rainy season. We conclude that highly susceptible cultivars play an important role in the spread of BXW and control measures should be effectively implemented during the rainy season if BXW is to be eradicated.

scholarly journals Rich Dynamics of an Epidemic Model with Saturation Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hui Wan ◽  
Jing-an Cui
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Medical Resource ◽  
Sir Epidemic Model ◽  
The Impact ◽  
The Basic Reproduction Number

A SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission. The basic reproduction number is identified. Existence and stability of equilibria are obtained under different conditions. Bifurcations, including backward bifurcation and Hopf bifurcation, are analyzed. Our results suggest that the model considering the impact of limited medical resource may exhibit vital dynamics, such as bistability and periodicity when the basic reproduction numberℝ0is less than unity, which implies that the basic reproductive number itself is not enough to describe whether the disease will prevail or not and a subthreshold number is needed. It is also shown that a sufficient number of sickbeds and other medical resources are very important for disease control and eradication. Considering the costs, we provide a method to estimate a suitable treatment capacity for a disease in a region.

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