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1.
A new deterministic model is designed and used to assess the community-wide impact of mass vaccination of new sexually active individuals on the dynamics of the oncogenic and warts-causing HPV types. Rigorous qualitative analyses of the model, which incorporates the two currently available anti-HPV vaccines, reveal that it undergoes competitive exclusion when the reproduction of one HPV risk type (low/high) exceeds unity, while that of the other HPV risk type is less than unity. For the case when the reproduction numbers of the two HPV risk types (low/high) exceed unity, the two risk types co-exist. It is shown that the sub-model with the low-risk HPV types only has at least one endemic equilibrium whenever the associated reproduction threshold exceeds unity. Furthermore, this sub-model undergoes a re-infection-induced backward bifurcation under certain conditions. In the absence of the re-infection of recovered individuals and cancer-induced mortality in males, the associated disease-free equilibrium of the full (risk-structured) model is shown to be globally asymptotically stable whenever the reproduction number of the model is less than unity (that is, the full model does not undergo backward bifurcation under this setting). It is shown, via numerical simulations, that the use of the Gardasil vaccine could lead to the effective control of HPV in the community if the coverage rate is in the range of 73–95 % (84 %). If 70 % of the new sexually active susceptible females are vaccinated with the Gardasil vaccine, additionally vaccinating 34–56 % (45 %) of the new sexually active susceptible males can lead to the effective community-wide control (or elimination) of the HPV types. 相似文献
2.
Miranda I. Teboh-Ewungkem Chandra N. Podder Abba B. Gumel 《Bulletin of mathematical biology》2010,72(1):63-93
A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite)
in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features.
It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free
equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ0), is less than unity. Further, it has a unique endemic equilibrium if ℛ0>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses
of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease
burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with
a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛvac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine
if ℛvac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level
of gametocyte is critically important to the malaria burden in the community. 相似文献
3.
This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the number of infectives reaches the capacity. Under some conditions, it is shown that there exists a backward bifurcation from an endemic equilibrium, which implies that the disease-free equilibrium coexists with an endemic equilibrium. In such a case, reducing the basic reproduction number less than unity is not enough to control and eradicate the disease, extra measures are needed to ensure that the solutions approach the disease-free equilibrium. When the basic reproduction number is greater than unity, the model can have multiple endemic equilibria due to the effect of treatment, vaccination and other parameters. The existence and stability of the endemic equilibria of the model are analyzed and sufficient conditions on the existence and stability of a limit cycle are obtained. Numerical simulations are presented to illustrate the analytical results. 相似文献
4.
O. Sharomi C. N. Podder A. B. Gumel S. M. Mahmud E. Rubinstein 《Bulletin of mathematical biology》2011,73(3):515-548
The paper presents a deterministic compartmental model for the transmission dynamics of swine influenza (H1N1) pandemic in
a population in the presence of an imperfect vaccine and use of drug therapy for confirmed cases. Rigorous analysis of the
model, which stratifies the infected population in terms of their risk of developing severe illness, reveals that it exhibits
a vaccine-induced backward bifurcation when the associated reproduction number is less than unity. The epidemiological consequence of this result is that the effective control of H1N1, when the reproduction
number is less than unity, in the population would then be dependent on the initial sizes of the subpopulations of the model.
For the case where the vaccine is perfect, it is shown that having the reproduction number less than unity is necessary and
sufficient for effective control of H1N1 in the population (in such a case, the associated disease-free equilibrium is globally
asymptotically stable). The model has a unique endemic equilibrium when the reproduction number exceeds unity. Numerical simulations
of the model, using data relevant to the province of Manitoba, Canada, show that it reasonably mimics the observed H1N1 pandemic
data for Manitoba during the first (Spring) wave of the pandemic. Further, it is shown that the timely implementation of a
mass vaccination program together with the size of the Manitoban population that have preexisting infection-acquired immunity
(from the first wave) are crucial to the magnitude of the expected burden of disease associated with the second wave of the
H1N1 pandemic. With an estimated vaccine efficacy of approximately 80%, it is projected that at least 60% of Manitobans need
to be vaccinated in order for the effective control or elimination of the H1N1 pandemic in the province to be feasible. Finally,
it is shown that the burden of the second wave of H1N1 is expected to be at least three times that of the first wave, and
that the second wave would last until the end of January or early February, 2010. 相似文献
5.
Epidemic control strategies alter the spread of the disease in the host population. In this paper, we describe and discuss mathematical models that can be used to explore the potential of pre-exposure and post-exposure vaccines currently under development in the control of tuberculosis. A model with bacille Calmette-Guerin (BCG) vaccination for the susceptibles and treatment for the infectives is first presented. The epidemic thresholds known as the basic reproduction numbers and equilibria for the models are determined and stabilities are investigated. The reproduction numbers for the models are compared to assess the impact of the vaccines currently under development. The centre manifold theory is used to show the existence of backward bifurcation when the associated reproduction number is less than unity and that the unique endemic equilibrium is locally asymptotically stable when the associated reproduction number is greater than unity. From the study we conclude that the pre-exposure vaccine currently under development coupled with chemoprophylaxis for the latently infected and treatment of infectives is more effective when compared to the post-exposure vaccine currently under development for the latently infected coupled with treatment of the infectives. 相似文献
6.
A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number [Formula: see text] is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels. Numerical simulations are carried out to show that when [Formula: see text], the unique endemic equilibrium can lose its stability and oscillations occur. Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically. 相似文献
7.
Andrew S. Azman Francisco J. Luquero Amabelia Rodrigues Pedro Pablo Palma Rebecca F. Grais Cunhate Na Banga Bryan T. Grenfell Justin Lessler 《PLoS neglected tropical diseases》2012,6(11)
Background
Use of cholera vaccines in response to epidemics (reactive vaccination) may provide an effective supplement to traditional control measures. In Haiti, reactive vaccination was considered but, until recently, rejected in part due to limited global supply of vaccine. Using Bissau City, Guinea-Bissau as a case study, we explore neighborhood-level transmission dynamics to understand if, with limited vaccine and likely delays, reactive vaccination can significantly change the course of a cholera epidemic.Methods and Findings
We fit a spatially explicit meta-population model of cholera transmission within Bissau City to data from 7,551 suspected cholera cases from a 2008 epidemic. We estimated the effect reactive vaccination campaigns would have had on the epidemic under different levels of vaccine coverage and campaign start dates. We compared highly focused and diffuse strategies for distributing vaccine throughout the city. We found wide variation in the efficiency of cholera transmission both within and between areas of the city. “Hotspots”, where transmission was most efficient, appear to drive the epidemic. In particular one area, Bandim, was a necessary driver of the 2008 epidemic in Bissau City. If vaccine supply were limited but could have been distributed within the first 80 days of the epidemic, targeting vaccination at Bandim would have averted the most cases both within this area and throughout the city. Regardless of the distribution strategy used, timely distribution of vaccine in response to an ongoing cholera epidemic can prevent cases and save lives.Conclusions
Reactive vaccination can be a useful tool for controlling cholera epidemics, especially in urban areas like Bissau City. Particular neighborhoods may be responsible for driving a city''s cholera epidemic; timely and targeted reactive vaccination at such neighborhoods may be the most effective way to prevent cholera cases both within that neighborhood and throughout the city. 相似文献8.
Elbasha EH 《Bulletin of mathematical biology》2008,70(3):894-909
Human papillomavirus (HPV) is the primary cause of cervical carcinoma and its precursor lesions, and is associated with a
variety of other cancers and diseases. A prophylactic quadrivalent vaccine against oncogenic HPV 16/18 and warts-causing genital
HPV 6/11 types is currently available in several countries. Licensure of a bivalent vaccine against oncogenic HPV 16/18 is
expected in the near future. This paper presents a two-sex, deterministic model for assessing the potential impact of a prophylactic
HPV vaccine with several properties. The model is based on the susceptible-infective-removed (SIR) compartmental structure.
Important epidemiological thresholds such as the basic and effective reproduction numbers and a measure of vaccine impact
are derived. We find that if the effective reproduction number is greater than unity, there is a locally unstable infection-free
equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the effective reproduction number is less
than unity, the infection-free equilibrium is globally asymptotically stable, and HPV will be eliminated. 相似文献
9.
Mathematical models have long been used to better understand disease transmission dynamics and how to effectively control
them. Here, a chancroid infection model is presented and analyzed. The disease-free equilibrium is shown to be globally asymptotically
stable when the reproduction number is less than unity. High levels of treatment are shown to reduce the reproduction number
suggesting that treatment has the potential to control chancroid infections in any given community. This result is also supported
by numerical simulations which show a decline in chancroid cases whenever the reproduction number is less than unity. 相似文献
10.
Shuaibu Ahijo Abdullahi Abdulrazaq Garba Habib Nafiu Hussaini 《PLoS neglected tropical diseases》2021,15(8)
A mathematical model is designed to assess the impact of some interventional strategies for curtailing the burden of snakebite envenoming in a community. The model is fitted with real data set. Numerical simulations have shown that public health awareness of the susceptible individuals on snakebite preventive measures could reduce the number of envenoming and prevent deaths and disabilities in the population. The simulations further revealed that if at least fifty percent of snakebite envenoming patients receive early treatment with antivenom a substantial number of deaths will be averted. Furthermore, it is shown using optimal control that combining public health awareness and antivenom treatment averts the highest number of snakebite induced deaths and disability adjusted life years in the study area. To choose the best strategy amidst limited resources in the study area, cost effectiveness analysis in terms of incremental cost effectiveness ratio is performed. It has been established that the control efforts of combining public health awareness of the susceptible individuals and antivenom treatment for victims of snakebite envenoming is the most cost effective strategy. Approximately the sum of US$72,548 is needed to avert 117 deaths or 2,739 disability adjusted life years that are recorded within 21 months in the study area. Thus, the combination of these two control strategies is recommended. 相似文献
11.
A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is
presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally
asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less
than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic
equilibria are locally asymptotically stable when the associated reproduction numbers are greater than unity. Qualitative
analysis of the model including positivity, boundedness and persistence of solutions are presented. The model is numerically
analysed to assess the effects of treatment with amelioration on the dynamics of a two strain HIV/AIDS model. Numerical simulations
of the model show that the two strains co-exist whenever the reproduction numbers exceed unity. Further, treatment with amelioration
may result in an increase in the total number of infective individuals (asymptomatic) but results in a decrease in the number
of AIDS patients. Further, analysis of the reproduction numbers show that antiretroviral resistance increases with increase
in antiretroviral use. 相似文献
12.
采用间接酶联免疫法,即用神经节苷脂包被,加入待检样品,再加入兔抗霍乱毒素B亚单位抗体,用标准样品的吸光值(A值)对标准样品的浓度绘制4-参数拟合曲线,根据标准曲线计算出待测样品中的CT浓度。结果显示,在浓度范围(0.6~16)ng/ml之间,CT标准浓度和检测浓度成线性关系,r2=0.9986。精确度在浓度范围(0.6~16)ng/ml,CT的平均回收率在96.24%~114.44%之间。精密度:批内变异CV%≤12.98%,批间变异CV%≤18.48%。特异性CT浓度在10ng/ml时,平均回收率为102.6%;CT浓度在5ng/ml时,平均回收率为111.17%;CT浓度在2.5ng/ml时,平均回收率为123.83%。实验表明该方法可检测霍乱疫苗原液中CT的含量。 相似文献
13.
Shantanu K. Kar Binod Sah Bikash Patnaik Yang Hee Kim Anna S. Kerketta Sunheang Shin Shyam Bandhu Rath Mohammad Ali Vittal Mogasale Hemant K. Khuntia Anuj Bhattachan Young Ae You Mahesh K. Puri Anna Lena Lopez Brian Maskery Gopinath B. Nair John D. Clemens Thomas F. Wierzba 《PLoS neglected tropical diseases》2014,8(2)
Introduction
The substantial morbidity and mortality associated with recent cholera outbreaks in Haiti and Zimbabwe, as well as with cholera endemicity in countries throughout Asia and Africa, make a compelling case for supplementary cholera control measures in addition to existing interventions. Clinical trials conducted in Kolkata, India, have led to World Health Organization (WHO)-prequalification of Shanchol, an oral cholera vaccine (OCV) with a demonstrated 65% efficacy at 5 years post-vaccination. However, before this vaccine is widely used in endemic areas or in areas at risk of outbreaks, as recommended by the WHO, policymakers will require empirical evidence on its implementation and delivery costs in public health programs. The objective of the present report is to describe the organization, vaccine coverage, and delivery costs of mass vaccination with a new, less expensive OCV (Shanchol) using existing public health infrastructure in Odisha, India, as a model.Methods
All healthy, non-pregnant residents aged 1 year and above residing in selected villages of the Satyabadi block (Puri district, Odisha, India) were invited to participate in a mass vaccination campaign using two doses of OCV. Prior to the campaign, a de jure census, micro-planning for vaccination and social mobilization activities were implemented. Vaccine coverage for each dose was ascertained as a percentage of the censused population. The direct vaccine delivery costs were estimated by reviewing project expenditure records and by interviewing key personnel.Results
The mass vaccination was conducted during May and June, 2011, in two phases. In each phase, two vaccine doses were given 14 days apart. Sixty-two vaccination booths, staffed by 395 health workers/volunteers, were established in the community. For the censused population, 31,552 persons (61% of the target population) received the first dose and 23,751 (46%) of these completed their second dose, with a drop-out rate of 25% between the two doses. Higher coverage was observed among females and among 6–17 year-olds. Vaccine cost at market price (about US$1.85/dose) was the costliest item. The vaccine delivery cost was $0.49 per dose or $1.13 per fully vaccinated person.Discussion
This is the first undertaken project to collect empirical evidence on the use of Shanchol within a mass vaccination campaign using existing public health program resources. Our findings suggest that mass vaccination is feasible but requires detailed micro-planning. The vaccine and delivery cost is affordable for resource poor countries. Given that the vaccine is now WHO pre-qualified, evidence from this study should encourage oral cholera vaccine use in countries where cholera remains a public health problem. 相似文献14.
Kbenesh W. Blayneh Abba B. Gumel Suzanne Lenhart Tim Clayton 《Bulletin of mathematical biology》2010,72(4):1006-1028
The paper considers a deterministic model for the transmission dynamics of West Nile virus (WNV) in the mosquito-bird-human
zoonotic cycle. The model, which incorporates density-dependent contact rates between the mosquito population and the hosts
(birds and humans), is rigorously analyzed using dynamical systems techniques and theories. These analyses reveal the existence
of the phenomenon of backward bifurcation (where the stable disease-free equilibrium of the model co-exists with a stable
endemic equilibrium when the reproduction number of the disease is less than unity) in WNV transmission dynamics. The epidemiological
consequence of backward bifurcation is that the classical requirement of having the reproduction number less than unity, while
necessary, is no longer sufficient for WNV elimination from the population. It is further shown that the model with constant
contact rates can also exhibit this phenomenon if the WNV-induced mortality in the avian population is high enough. The model
is extended to assess the impact of some anti-WNV control measures, by re-formulating the model as an optimal control problem
with density-dependent demographic parameters. This entails the use of two control functions, one for mosquito-reduction strategies
and the other for personal (human) protection, and redefining the demographic parameters as density-dependent rates. Appropriate
optimal control methods are used to characterize the optimal levels of the two controls. Numerical simulations of the optimal
control problem, using a set of reasonable parameter values, suggest that mosquito reduction controls should be emphasized
ahead of personal protection measures. 相似文献
15.
Mudassar Imran Hassan Rafique Adnan Khan Tufail Malik 《Theorie in den Biowissenschaften》2014,133(2):91-109
In this paper, we present a rigorous mathematical analysis of a deterministic model for the transmission dynamics of hepatitis C. The model is suitable for populations where two frequent modes of transmission of hepatitis C virus, namely unsafe blood transfusions and intravenous drug use, are dominant. The susceptible population is divided into two distinct compartments, the intravenous drug users and individuals undergoing unsafe blood transfusions. Individuals belonging to each compartment may develop acute and then possibly chronic infections. Chronically infected individuals may be quarantined. The analysis indicates that the eradication and persistence of the disease is completely determined by the magnitude of basic reproduction number R c. It is shown that for the basic reproduction number R c < 1, the disease-free equilibrium is locally and globally asymptotically stable. For R c > 1, an endemic equilibrium exists and the disease is uniformly persistent. In addition, we present the uncertainty and sensitivity analyses to investigate the influence of different important model parameters on the disease prevalence. When the infected population persists, we have designed a time-dependent optimal quarantine strategy to minimize it. The Pontryagin’s Maximum Principle is used to characterize the optimal control in terms of an optimality system which is solved numerically. Numerical results for the optimal control are compared against the constant controls and their efficiency is discussed. 相似文献
16.
In the absence of valid medicine or vaccine for treating the pandemic Coronavirus (COVID-19) infection, other control strategies like; quarantine, social distancing, self- isolation, sanitation and use of personal protective equipment are effective tool used to prevent and curtail the spread of the disease. In this paper, we present a mathematical model to study the dynamics of COVID-19. We then formulate an optimal control problem with the aim to study the most effective control strategies to prevent the proliferation of the disease. The existence of an optimal control function is established and the Pontryagin maximum principle is applied for the characterization of the controller. The equilibrium solutions (DFE & endemic) are found to be locally asymptotically stable and subsequently the basic reproduction number is obtained. Numerical simulations are carried out to support the analytic results and to explicitly show the significance of the control. It is shown that Quarantine/isolating those infected with the disease is the best control measure at the moment. 相似文献
17.
A staged-progression HIV model is formulated and used to investigate the potential impact of an imperfect vaccine. The vaccine
is assumed to have several desirable characteristics such as protecting against infection, causing bypass of the primary infection
stage, and offering a disease-altering therapeutic effect (so that the vaccine induces reversal from the full blown AIDS stage
to the asymptomatic stage). The model, which incorporates HIV transmission by individuals in the AIDS stage, is rigorously
analyzed to gain insight into its qualitative features. Using a comparison theorem, the model with mass action incidence is
shown to have a globally-asymptotically stable disease-free equilibrium whenever a certain threshold, known as the vaccination reproduction number, is less than unity. Furthermore, the model with mass action incidence has a unique endemic equilibrium whenever this threshold
exceeds unity. Using the Li-Muldowney techniques for a reduced version of the mass action model, this endemic equilibrium
is shown to be globally-asymptotically stable, under certain parameter restrictions. The epidemiological implications of these
results are that an imperfect vaccine can eliminate HIV in a given community if it can reduce the reproduction number to a
value less than unity, but the disease will persist otherwise. Furthermore, a future HIV vaccine that induces the bypass of
primary infection amongst vaccinated individuals (who become infected) would decrease HIV prevalence, whereas a vaccine with
therapeutic effect could have a positive or negative effect at the community level. 相似文献
18.
Cholera, an acute gastro-intestinal infection and a waterborne disease continues to emerge in developing countries and remains an important global health challenge. We formulate a mathematical model that captures some essential dynamics of cholera transmission to study the impact of public health educational campaigns, vaccination and treatment as control strategies in curtailing the disease. The education-induced, vaccination-induced and treatment-induced reproductive numbers R(E), R(V), R(T) respectively and the combined reproductive number R(C) are compared with the basic reproduction number R(0) to assess the possible community benefits of these control measures. A Lyapunov functional approach is also used to analyse the stability of the equilibrium points. We perform sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Graphical representations are provided to qualitatively support the analytical results. 相似文献
19.
O139霍乱灭活全菌体菌苗免疫后人群抗体水平测定 总被引:3,自引:0,他引:3
O139霍乱弧菌经甲醛灭活制备而成的全菌体菌苗在广西田阳县进行临床考核。每组50名中学生经肌肉途径接种45亿菌和90亿菌两种剂量,一个月后80%接种者血清中杀弧菌抗体升高,最高可达1∶160,免疫后3个月开始缓慢下降,但仍有68-72%接种者抗体效价在1∶20以上。高剂量组半数接种者的杀弧菌抗体可维持存在6个月。血清中凝集抗体升高明显,但3个月后下降也明显。与对照组O1菌苗相比,两种抗体水平升高与下降趋势一致。采用ELISA法测定抗毒抗体,O139菌苗组与O1菌苗组结果相似,均有一定上升。上述结果提示O139霍乱灭活菌苗可作为短效应急菌苗使用 相似文献
20.
Rachael L. Miller Neilan Elsa Schaefer Holly Gaff K. Renee Fister Suzanne Lenhart 《Bulletin of mathematical biology》2010,72(8):2004-2018
While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate
a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class
for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic reproductive number
from multiple infectious classes. Using optimal control theory, parameter sensitivity analysis, and numerical simulations,
a cost-effective balance of multiple intervention methods is compared for two endemic populations. Results provide a framework
for designing cost-effective strategies for diseases with multiple intervention methods. 相似文献