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.

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 Sensitivity, Optimal Control, and Cost-Effectiveness Analysis of Intervention Strategies of Filariasis

2022 ◽  
Vol 4 (1) ◽  
pp. 64-76
Author(s):  
Darmawati Darmawati ◽  
Musafira Musafira ◽  
Darma Ekawati ◽  
Wahyudin Nur ◽  
Muhlis Muhlis ◽  
...  
Keyword(s):  
Cost Effectiveness ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Cost Effective ◽  
Intervention Strategies ◽  
Bed Net ◽  
Effective Strategy ◽  
Cost Effective Strategy ◽  
Net Use ◽  
The Basic Reproduction Number

In this work, sensitivity, optimal control, and cost-effectiveness of several intervention strategies of filariasis are discussed. We study the intervention strategies that are related to bednet use, insecticide, and the combination of bed-net use and insecticide. We use Pontryagin’s maximum principle to characterize the optimal controls. The Average Cost-Effectiveness Ratio (ACER) and Infection Averted Ratio (IAR) are used to identify the most cost-effective strategy. We also determine the basic reproduction number and investigate the sensitivity of the basic reproduction number on the parameters that are related to bed-net use and insecticide. Based on the ACER values, the most cost-effective strategy to control filariasis is insecticide intervention. On the other hand, the IAR values indicates that bed-net use intervention is the most cost-effective strategy. Furthermore, it is also the most effective strategy to eliminate filariasis. The sensitivity analysis results show that the control parameter related to bed net use and treatment have a central role in reducing the basic reproduction number and filariasis spread.

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 Government control in increasing vehicles taxpayer compliance

2021 ◽  
Vol 26 ◽  
pp. 502-513
Author(s):  
Diah Anggeraini Hasri ◽  
Zulkieflimansyah Zulkieflimansyah ◽  
Muhammad Nurjihadi ◽  
Nova Adhitya Ananda ◽  
Lukmanul Hakim
Keyword(s):  
Mathematical Model ◽  
Regression Analysis ◽  
Differential Equations ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sensitivity Index ◽  
Control Parameters ◽  
Government Control ◽  
Analysis Tools ◽  
The Basic Reproduction Number

This study aims to determine the dynamics of taxpayer compliance from time to time by using a mathematical model. This study uses two analysis tools, namely differential equations, to create a model of taxpayer compliance and Moderated Regression Analysis to determine the effect of moderating government control on increasing taxpayer compliance. This study indicates that government control can reduce the number of non-compliant taxpayers by looking at the sensitivity index. The results of the sensitivity index of government control parameters can reduce the basic reproduction number. Statistically, it is also proven that the moderation of government control can strengthen the effect of awareness on taxpayer compliance by 82.5%.

scholarly journals Mathematical modelling and optimal cost-effective control of COVID-19 transmission dynamics

2020 ◽  
Author(s):  
S. Olaniyi ◽  
O.S. Obabiyi ◽  
K.O. Okosun ◽  
A.T. Oladipo ◽  
S.O. Adewale
Keyword(s):  
Basic Reproduction Number ◽  
Least Squares Method ◽  
Reproduction Number ◽  
Cost Effective ◽  
Effective Control ◽  
Cumulative Number ◽  
The Novel ◽  
Novel Coronavirus ◽  
Disease Free ◽  
The Basic Reproduction Number

Abstract The novel coronavirus disease (COVID-19) caused by a new strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remains the current global health challenge. In this paper, an epidemic model based on system of ordinary differential equations is formulated by taking into account the transmission routes from symptomatic, asymptomatic and hospitalized individuals. The model is fitted to the corresponding cumulative number of hospitalized individuals (active cases) reported by the Nigeria Centre for Disease Control (NCDC), and parameterized using the least squares method. The basic reproduction number which measures the potential spread of COVID-19 in the population is computed using the next generation operator method. Further, Lyapunov function is constructed to investigate the stability of the model around a disease-free equilibrium point. It is shown that the model has a globally asymptotically stable disease-free equilibrium if the basic reproduction number of the novel coronavirus transmission is less than one. Sensitivities of the model to changes in parameters are explored. It is revealed further that the basic reproduction number can be brought to a value less than one in Nigeria, if the current effective transmission rate of the disease can be reduced by 50%. Otherwise, the number of active cases may get up to 2.5% of the total estimated population. In addition, two time-dependent control variables, namely preventive and management measures, are considered to mitigate the damaging effects of the disease using Pontryagin's maximum principle. The most cost-effective control measure is determined through cost-effectiveness analysis. Numerical simulations of the overall system are implemented in MatLab® for demonstration of the theoretical results.

scholarly journals Estimation of the basic reproduction number of novel coronavirus (COVID-19) in Bangladesh: A 65-day outbreak data-driven analysis

2020 ◽  
Author(s):  
Md. Hasan ◽  
Akhtar Hossain ◽  
Wasimul Bari ◽  
Syed Shariful Islam
Keyword(s):  
Growth Model ◽  
Basic Reproduction Number ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Fold Increase ◽  
Reporting Rate ◽  
Basic Reproductive Number ◽  
Exponential Growth Model ◽  
Novel Coronavirus ◽  
The Basic Reproduction Number

Abstract BackgroundThe outbreak of novel coronavirus disease (COVID-19), started from Wuhan, China, at the end of December 2019, hits almost the entire world. In Bangladesh, the first case was officially reported on March 8, 2020. We estimated the basic reproductive number, R0, of COVID-19 for Bangladesh using the first 65-day data of the outbreak.MethodsWith time-varying disease reporting rate, epidemic curves were estimated using the exponential growth model utilizing daily COVID-19 diagnosis data in Bangladesh from March 8 to May 11, 2020. We estimated R0 using the estimated intrinsic growth rate (γ). Serial intervals (SI) have been used from two well-known coronaviruses’ outbreaks, SARS and MERS; and the early estimate of SI of COVID-19 in Wuhan, China.ResultsThe COVID-19 epidemic in Bangladesh followed an exponential growth model. We found the R0 to be 1.84 [95% CI: 1.82–1.86], 1.82 [95% CI: 1.81–1.84], and 1.94 [95% CI: 1.92–1.96], for MERS, COVID-19, and SARS SI respectively without adjusting reporting rate. With the adjusted reporting rate, R0 reduced to 1.63 [95% CI: 1.62–1.65], 1.62 [95% CI: 1.61–1.64], and 1.71 [95% CI: 1.70–1.73] for a five-fold increase. Inverse association between the reporting rate and the basic reproduction number was observed.ConclusionThe R0 was found to be 1.87 for existing cases and was reduced to 1.65 for the five-fold increase of the early reporting rate. Findings suggest a continued COVID-19 outbreak in Bangladesh and immediate steps need to be taken to control.

scholarly journals A model for COVID-19 with isolation, quarantine and testing as control measures

2020 ◽  
Author(s):  
M.S. Aronna ◽  
R. Guglielmi ◽  
L.M. Moschen
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Risk Groups ◽  
Control Measures ◽  
Contact Rate ◽  
Control Parameters ◽  
Social Distancing ◽  
Proposed Model ◽  
Asymptomatic Infections ◽  
The Basic Reproduction Number

AbstractIn this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. We refer to quarantine as strict isolation, and it is applied to confirmed infected cases.In the proposed model, the proportion of people in isolation, the level of contact reduction and the testing rate are control parameters that can vary in time, representing policies that evolve in different stages. We obtain an explicit expression for the basic reproduction number in terms of the parameters of the disease and of the control policies. In this way we can quantify the effect that isolation and testing have in the evolution of the epidemic. We present a series of simulations to illustrate different realistic scenarios. From the expression of and the simulations we conclude that isolation (social distancing) and testing among asymptomatic cases are fundamental actions to control the epidemic, and the stricter these measures are and the sooner they are implemented, the more lives can be saved. Additionally, we show that people that remain in isolation significantly reduce their probability of contagion, so risk groups should be recommended to maintain a low contact rate during the course of the epidemic.

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.

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