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 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 Time from Symptom Onset to Hospitalisation of Coronavirus Disease 2019 (COVID-19) Cases: Implications for the Proportion of Transmissions from Infectors with Few Symptoms

2020 ◽  
Vol 9 (5) ◽  
pp. 1297 ◽  
Author(s):  
Robin N. Thompson ◽  
Francesca A. Lovell-Read ◽  
Uri Obolski
Keyword(s):  
Basic Reproduction Number ◽  
Symptom Onset ◽  
Reproduction Number ◽  
Wide Spectrum ◽  
Control Measures ◽  
Current Evidence ◽  
The Novel ◽  
Novel Coronavirus ◽  
The Basic Reproduction Number

Interventions targeting symptomatic hosts and their contacts were successful in bringing the 2003 SARS pandemic under control. In contrast, the COVID-19 pandemic has been harder to contain, partly because of its wide spectrum of symptoms in infectious hosts. Current evidence suggests that individuals can transmit the novel coronavirus while displaying few symptoms. Here, we show that the proportion of infections arising from hosts with few symptoms at the start of an outbreak can, in combination with the basic reproduction number, indicate whether or not interventions targeting symptomatic hosts are likely to be effective. However, as an outbreak continues, the proportion of infections arising from hosts with few symptoms changes in response to control measures. A high proportion of infections from hosts with few symptoms after the initial stages of an outbreak is only problematic if the rate of new infections remains high. Otherwise, it can simply indicate that symptomatic transmissions are being prevented successfully. This should be considered when interpreting estimates of the extent of transmission from hosts with few COVID-19 symptoms.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

2020 ◽  
Vol 28 (02) ◽  
pp. 351-376 ◽  
Author(s):  
MUHAMMAD ALTAF KHAN ◽  
SYED AZHAR ALI SHAH ◽  
SAIF ULLAH ◽  
KAZEEM OARE OKOSUN ◽  
MUHAMMAD FAROOQ
Keyword(s):  
Optimal Control ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Control Strategies ◽  
Control Measures ◽  
Hepatitis B Infection ◽  
Control Variables ◽  
Effect Of Treatment ◽  
The Basic Reproduction Number

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

scholarly journals Global stability analysis and control of leptospirosis

2016 ◽  
Vol 14 (1) ◽  
pp. 567-585 ◽  
Author(s):  
Kazeem Oare Okosun ◽  
M. Mukamuri ◽  
Daniel Oluwole Makinde
Keyword(s):  
Cost Effectiveness ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Cost Effective ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Parameters ◽  
Constant Control ◽  
Preventive Vaccination ◽  
The Basic Reproduction Number

AbstractThe aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters’ case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model’s parameters are calculated. In the time-dependent constant control case, Pontryagin’s Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

scholarly journals Estimating the basic reproduction number for the 2015 bubonic plague outbreak in Nyimba district of Eastern Zambia

2020 ◽  
Vol 14 (11) ◽  
pp. e0008811
Author(s):  
Joseph Sichone ◽  
Martin C. Simuunza ◽  
Bernard M. Hang’ombe ◽  
Mervis Kikonko
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Cost Effective ◽  
Control Measures ◽  
Effective Control ◽  
Infectious Period ◽  
Bubonic Plague ◽  
Infectious Individual ◽  
Susceptible Population ◽  
The Basic Reproduction Number

Background Plague is a re-emerging flea-borne infectious disease of global importance and in recent years, Zambia has periodically experienced increased incidence of outbreaks of this disease. However, there are currently no studies in the country that provide a quantitative assessment of the ability of the disease to spread during these outbreaks. This limits our understanding of the epidemiology of the disease especially for planning and implementing quantifiable and cost-effective control measures. To fill this gap, the basic reproduction number, R0, for bubonic plague was estimated in this study, using data from the 2015 Nyimba district outbreak, in the Eastern province of Zambia. R0 is the average number of secondary infections arising from a single infectious individual during their infectious period in an entirely susceptible population. Methodology/Principal findings Secondary epidemic data for the most recent 2015 Nyimba district bubonic plague outbreak in Zambia was analyzed. R0 was estimated as a function of the average epidemic doubling time based on the initial exponential growth rate of the outbreak and the average infectious period for bubonic plague. R0 was estimated to range between 1.5599 [95% CI: 1.382–1.7378] and 1.9332 [95% CI: 1.6366–2.2297], with average of 1.7465 [95% CI: 1.5093–1.9838]. Further, an SIR deterministic mathematical model was derived for this infection and this estimated R0 to be between 1.4 to 1.5, which was within the range estimated above. Conclusions/Significance This estimated R0 for bubonic plague is an indication that each bubonic plague case can typically give rise to almost two new cases during these outbreaks. This R0 estimate can now be used to quantitatively analyze and plan measurable interventions against future plague outbreaks in Zambia.

Dynamics of synthetic drug transmission models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shitao Liu ◽  
Liang Zhang
Keyword(s):  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
History Of ◽  
Synthetic Drug ◽  
Transmission Models ◽  
The Basic Reproduction Number

Abstract The deterministic and stochastic synthetic drug transmission models with relapse are formulated. For the deterministic model, the basic reproduction number R 0 is derived. We show that if R 0 < 1, the drug-free equilibrium is globally asymptotically stable and if R 0 > 1, there exists a unique drug-addition equilibrium which is globally asymptotically stable. For the stochastic model, we show there exists a unique global positive solution of the stochastic model for any positive initial value. Then by constructing some stochastic Lyapunov functions, we show that the solution of the stochastic model is going around each of the steady states of the corresponding deterministic model under certain parametric conditions. The sensitive analysis of the basic reproduction number R 0 indicates that it is helpful to reduce the relapse rate of people who have a history of drug abuse in the control of synthetic drug spreading. Numerical simulations are carried out and approve our results.

scholarly journals The effect of control measures on COVID-19 transmission in Italy: Comparison with Guangdong province in China

2020 ◽  
Author(s):  
Peiyu Liu ◽  
Sha He ◽  
Libin Rong ◽  
Sanyi Tang
Keyword(s):  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Control Measures ◽  
Seir Model ◽  
Diagnosis Rate ◽  
And Control ◽  
Parameter Values ◽  
Test Result ◽  
The Basic Reproduction Number

Abstract Background COVID-19 is spreading in many countries around the world. Italy is the hardest hit in Europe and its number of new infections is still increasing. This study aims to evaluate the reason for the rapidly growing epidemic in Italy.Methods We compared Italy’s data of outbreak and control measures with the province of Guangdong in China. Then, a modified SEIR model was applied to estimate the basic reproduction number. Finally, we utilized a time-dependent dynamic model to study the future disease dynamics in Italy.Results The comparison of specific measures implemented in the two places and the time when the measures were initiated shows that the prevention and control actions in Italy were not sufficiently timely and effective. Using a modified SEIR model, we estimated parameter values based on available cumulative data and calculate the basic reproduction number to be 4.32 before the national lockdown in Italy. Numerical simulations revealed that under a scenario in which very strict interventions are taken when the minimum contact rate is 1 with the exponential decreasing rate is 0.5 and the fast diagnosis rate is 0.5 with the exponential increasing rate is 0.5 (i.e. the test result will be available in two days). In this scenario, Italy will reach the peak (i.e. 23900) after 43 days.Conclusion This study suggests that Italy is currently in a very serious epidemic status since control measures such as blockade of schools, isolation, medical supports and media coverage are not sufficiently timely and effective.

scholarly journals Mathematical Model for Optimal Control of Soil-Transmitted Helminth Infection

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Health Education ◽  
Basic Reproduction Number ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Control Measures ◽  
Personal Hygiene ◽  
Susceptible Population ◽  
The Basic Reproduction Number

In this paper, we study the dynamics of soil-transmitted helminth infection. We formulate and analyse a deterministic compartmental model using nonlinear differential equations. The basic reproduction number is obtained and both disease-free and endemic equilibrium points are shown to be asymptotically stable under given threshold conditions. The model may exhibit backward bifurcation for some parameter values, and the sensitivity indices of the basic reproduction number with respect to the parameters are determined. We extend the model to include control measures for eradication of the infection from the community. Pontryagian’s maximum principle is used to formulate the optimal control problem using three control strategies, namely, health education through provision of educational materials, educational messages to improve the awareness of the susceptible population, and treatment by mass drug administration that target the entire population(preschool- and school-aged children) and sanitation through provision of clean water and personal hygiene. Numerical simulations were done using MATLAB and graphical results are displayed. The cost effectiveness of the control measures were done using incremental cost-effective ratio, and results reveal that the combination of health education and sanitation is the best strategy to combat the helminth infection. Therefore, in order to completely eradicate soil-transmitted helminths, we advise investment efforts on health education and sanitation controls.

scholarly journals The Cost-Effectiveness Analysis and Optimal Strategy of the Tobacco Control

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Liuyong Pang ◽  
Sanhong Liu ◽  
Xinan Zhang ◽  
Tianhai Tian
Keyword(s):  
Smoking Cessation ◽  
Cost Effectiveness ◽  
Basic Reproduction Number ◽  
Media Coverage ◽  
Reproduction Number ◽  
Control Measures ◽  
Smoking Cessation Treatment ◽  
Cessation Treatment ◽  
The Cost ◽  
The Basic Reproduction Number

This paper aims at investigating how the media coverage and smoking cessation treatment should be implemented, for a certain period, to reduce the numbers of smokers and patients caused by smoking while minimizing the total cost. To this end, we first propose a new mathematical model without any control strategies to investigate the dynamic behaviors of smoking. Furthermore, we calculate the basic reproduction number R0 and discuss the global asymptotic stabilities of the equilibria. Then, from the estimated parameter values, we know that the basic reproduction number R0 is more than 1, which reveals that smoking is one of the enduring problems of the society. Hence, we introduce two control measures (media coverage and smoking cessation treatment) into the model. Finally, in order to investigate their effects in smoking control and provide an analytical method for the strategic decision-makers, we apply a concrete example to calculate the incremental cost-effectiveness ratios and analyze the cost-effectiveness of all possible combinations of the two control measures. The results indicate that the combination of media coverage and smoking cessation treatment is the most cost-effective strategy for tobacco control.

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.

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