RESUMO
Virus proliferation involves gene replication inside infected cells and transmission to new target cells. Once positive-strand RNA virus has infected a cell, the viral genome serves as a template for copying ("stay-strategy") or is packaged into a progeny virion that will be released extracellularly ("leave-strategy"). The balance between genome replication and virion release determines virus production and transmission efficacy. The ensuing trade-off has not yet been well characterized. In this study, we use hepatitis C virus (HCV) as a model system to study the balance of the two strategies. Combining viral infection cell culture assays with mathematical modeling, we characterize the dynamics of two different HCV strains (JFH-1, a clinical isolate, and Jc1-n, a laboratory strain), which have different viral release characteristics. We found that 0.63% and 1.70% of JFH-1 and Jc1-n intracellular viral RNAs, respectively, are used for producing and releasing progeny virions. Analysis of the Malthusian parameter of the HCV genome (i.e., initial proliferation rate) and the number of de novo infections (i.e., initial transmissibility) suggests that the leave-strategy provides a higher level of initial transmission for Jc1-n, whereas, in contrast, the stay-strategy provides a higher initial proliferation rate for JFH-1. Thus, theoretical-experimental analysis of viral dynamics enables us to better understand the proliferation strategies of viruses, which contributes to the efficient control of virus transmission. Ours is the first study to analyze the stay-leave trade-off during the viral life cycle and the significance of the replication-release switching mechanism for viral proliferation.
Assuntos
Genoma Viral , Hepacivirus/genética , Interações Hospedeiro-Patógeno/genética , Envelhecimento/fisiologia , Linhagem Celular Tumoral , Proliferação de Células/genética , Hepatite C , Humanos , Modelos Biológicos , Replicação Viral/genéticaRESUMO
In this paper, we show how to modify a compartmental epidemic model, without changing the dimension, such that separable static heterogeneity is taken into account. The derivation is based on the Kermack-McKendrick renewal equation.
Assuntos
Epidemias , Modelos Biológicos , Modelos EpidemiológicosRESUMO
In the previous paper (Inaba in J Math Biol 65:309-348, 2012), we proposed a new (most biologically natural) definition of the basic reproduction number [Formula: see text] for structured population in general time-heterogeneous environments based on the generation evolution operator. Using the mathematical definition for cone spectral radius, we show that our [Formula: see text] is given by the spectral radius of the generation evolution operator in the time-state space. Then as far as we consider linear population dynamics, our [Formula: see text] is a threshold value for population extinction and persistence in time-heterogeneous environments. Next we prove that even for nonlinear systems, our [Formula: see text] plays a role of a threshold value for population extinction in time-heterogeneous environments. For periodic systems, we can show that supercritical condition [Formula: see text] implies existence of positive periodic solution. Finally using the idea of [Formula: see text] in time-heterogeneous environment, we examine existence and stability of periodic solution in the age-structured SIS epidemic model with time-periodic parameters.
Assuntos
Número Básico de Reprodução , Epidemias/prevenção & controle , Modelos Biológicos , Simulação por Computador , Humanos , Dinâmica Populacional , Fatores de TempoRESUMO
In this paper, we formulate an age-structured epidemic model for the demographic transition in which we assume that the cultural norms leading to lower fertility are transmitted amongst individuals in the same way as infectious diseases. First, we formulate the basic model as an abstract homogeneous Cauchy problem on a Banach space to prove the existence, uniqueness, and well-posedness of solutions. Next based on the normalization arguments, we investigate the existence of nontrivial exponential solutions and then study the linearized stability at the exponential solutions using the idea of asynchronous exponential growth. The relative stability defined in the normalized system and the absolute (orbital) stability in the original system are examined. For the boundary exponential solutions corresponding to infection-free or totally infected status, we formulate the stability condition using reproduction numbers. We show that bi-unstability of boundary exponential solutions is one of conditions which guarantee the existence of coexistent exponential solutions.
Assuntos
Epidemias/estatística & dados numéricos , Modelos Biológicos , Dinâmica Populacional/estatística & dados numéricos , Fatores Etários , Número Básico de Reprodução/estatística & dados numéricos , Doenças Transmissíveis/epidemiologia , Doenças Transmissíveis/transmissão , Simulação por Computador , Suscetibilidade a Doenças/epidemiologia , Feminino , Fertilidade , Humanos , Masculino , Conceitos Matemáticos , Dinâmica Populacional/tendênciasRESUMO
BACKGROUND: There has been a variation in published opinions toward the effectiveness of school closure which is implemented reactively when substantial influenza transmissions are seen at schools. Parameterizing an age-structured epidemic model using published estimates of the pandemic H1N1-2009 and accounting for the cost effectiveness, we examined if the timing and length of school closure could be optimized. METHODS: Age-structured renewal equation was employed to describe the epidemic dynamics of an influenza pandemic. School closure was assumed to take place only once during the course of the pandemic, abruptly reducing child-to-child transmission for a fixed length of time and also influencing the transmission between children and adults. Public health effectiveness was measured by reduction in the cumulative incidence, and cost effectiveness was also examined by calculating the incremental cost effectiveness ratio and adopting a threshold of 1.0 × 107 Japanese Yen/life-year. RESULTS: School closure at the epidemic peak appeared to yield the largest reduction in the final size, while the time of epidemic peak was shown to depend on the transmissibility. As the length of school closure was extended, we observed larger reduction in the cumulative incidence. Nevertheless, the cost effectiveness analysis showed that the cost of our school closure scenario with the parameters derived from H1N1-2009 was not justifiable. If the risk of death is three times or greater than that of H1N1-2009, the school closure could be regarded as cost effective. CONCLUSIONS: There is no fixed timing and duration of school closure that can be recommended as universal guideline for different types of influenza viruses. The effectiveness of school closure depends on the transmission dynamics of a particular influenza virus strain, especially the virulence (i.e. the infection fatality risk).
Assuntos
Análise Custo-Benefício , Surtos de Doenças , Influenza Humana/epidemiologia , Modelos Teóricos , Instituições Acadêmicas , Criança , Humanos , Influenza Humana/transmissão , Prática de Saúde PúblicaRESUMO
In the context of mathematical epidemiology, the type-reproduction number (TRN) for a specific host type is interpreted as the average number of secondary cases of that type produced by the primary cases of the same host type during the entire course of infection. Here, it must be noted that T takes into account not only the secondary cases directly transmitted from the specific host but also the cases indirectly transmitted by way of other types, who were infected from the primary cases of the specific host with no intermediate cases of the target host. Roberts and Heesterbeek (Proc R Soc Lond B 270:1359-1364, 2003) have shown that T is a useful measure when a particular single host type is targeted in the disease control effort in a community with various types of host, based on the fact that the sign relation sign(R0-1) = sign(T-1) holds between the basic reproduction number R0 and T. In fact, T can be seen as an extension of R0 in a sense that the threshold condition of the total population growth can be formulated by the reproduction process of the target type only. However, the original formulation is limited to populations with discrete state space in constant environments. In this paper, based on a new perspective of R0 in heterogeneous environments (Inaba in J Math Biol 2011), we give a general definition of the TRN for continuously structured populations in heterogeneous environments and show some examples of its computation and applications.
Assuntos
Número Básico de Reprodução , Doenças Transmissíveis/epidemiologia , Surtos de Doenças , Ecossistema , Interações Hospedeiro-Patógeno , Doenças Transmissíveis/transmissão , HumanosRESUMO
In this paper, we examine the stability of an endemic equilibrium in a chronological age-structured SIR (susceptible, infectious, removed) epidemic model with age-dependent infectivity. Under the assumption that the transmission rate is a shifted exponential function, we perform a Hopf bifurcation analysis for the endemic equilibrium, which uniquely exists if the basic reproduction number is greater than 1. We show that if the force of infection in the endemic equilibrium is equal to the removal rate, then there always exists a critical value such that a Hopf bifurcation occurs when the bifurcation parameter reaches the critical value. Moreover, even in the case where the force of infection in the endemic equilibrium is not equal to the removal rate, we show that if the distance between them is sufficiently small, then a similar Hopf bifurcation can occur. By numerical simulation, we confirm a special case where the stability switch of the endemic equilibrium occurs more than once.
Assuntos
Epidemias , Modelos Biológicos , Simulação por Computador , Número Básico de ReproduçãoRESUMO
Although its usefulness and possibility of the well-known definition of the basic reproduction number R0 for structured populations by Diekmann, Heesterbeek and Metz (J Math Biol 28:365-382, 1990) (the DHM definition) have been widely recognized mainly in the context of epidemic models, originally it deals with population dynamics in a constant environment, so it cannot be applied to formulate the threshold principle for population growth in time-heterogeneous environments. Since the mid-1990s, several authors proposed some ideas to extend the definition of R0 to the case of a periodic environment. In particular, the definition of R0 in a periodic environment by Bacaër and Guernaoui (J Math Biol 53:421-436, 2006) (the BG definition) is most important, because their definition of periodic R0 can be interpreted as the asymptotic per generation growth rate, which is an essential feature of the DHM definition. In this paper, we introduce a new definition of R0 based on the generation evolution operator (GEO), which has intuitively clear biological meaning and can be applied to structured populations in any heterogeneous environment. Using the generation evolution operator, we show that the DHM definition and the BG definition completely allow the generational interpretation and, in those two cases, the spectral radius of GEO equals the spectral radius of the next generation operator, so it gives the basic reproduction number. Hence the new definition is an extension of the DHM definition and the BG definition. Finally we prove a weak sign relation that if the average Malthusian parameter exists, it is nonnegative when R0>1 and it is nonpositive when R0<1.
Assuntos
Número Básico de Reprodução , Modelos Biológicos , Crescimento Demográfico , Surtos de Doenças , Fertilidade , HumanosRESUMO
Japan has been facing a population decline since 2010 due to low birth rates, interregional migration, and regional traits. In this study, we modeled the demographic dynamics of Japan using a transition matrix model. Then, from the mathematical structure of the model, we quantitatively evaluated the domestic factors of population decline. To achieve this, we constructed a multi-regional Leslie matrix model and developed a method for representing the reproductive value and stable age distribution using matrix entries. Our method enabled us to interpret the mathematical indices using the genealogies of the migration history of individuals and their ancestors. Furthermore, by combining our method with sensitivity analysis, we analyzed the effect of region-specific fertility rates and interregional migration rates on the population decline in Japan. We found that the sensitivity of the population growth rate to the migration rate from urban areas with large populations to prefectures with high fertility rates was greatest for people aged under 30. In addition, compared to other areas, the fertility rates of urban areas exhibited higher sensitivity for people aged over 30. Because this feature is robust in comparison with those in 2010 and 2015, it can be said to be a unique structure in Japan in recent years. We also established a method to represent the reproductive value and stable age distribution in an irreducible non-negative matrix population model by using the matrix entries. Furthermore, we show the effects of fertility and migration rates numerically in urban and non-urban areas on the population growth rates for each age group in a society with a declining population.
Assuntos
Coeficiente de Natalidade , Fertilidade , Adulto , Idoso , Animais , Humanos , Japão , Dinâmica Populacional , Projetos de PesquisaRESUMO
Empirical estimates of the incubation period of influenza A (H1N1-2009) have been limited. We estimated the incubation period among confirmed imported cases who traveled to Japan from Hawaii during the early phase of the 2009 pandemic (n=72). We addressed censoring and employed an infection-age structured argument to explicitly model the daily frequency of illness onset after departure. We assumed uniform and exponential distributions for the frequency of exposure in Hawaii, and the hazard rate of infection for the latter assumption was retrieved, in Hawaii, from local outbreak data. The maximum likelihood estimates of the median incubation period range from 1.43 to 1.64 days according to different modeling assumptions, consistent with a published estimate based on a New York school outbreak. The likelihood values of the different modeling assumptions do not differ greatly from each other, although models with the exponential assumption yield slightly shorter incubation periods than those with the uniform exposure assumption. Differences between our proposed approach and a published method for doubly interval-censored analysis highlight the importance of accounting for the dependence of the frequency of exposure on the survival function of incubating individuals among imported cases. A truncation of the density function of the incubation period due to an absence of illness onset during the exposure period also needs to be considered. When the data generating process is similar to that among imported cases, and when the incubation period is close to or shorter than the length of exposure, accounting for these aspects is critical for long exposure times.
Assuntos
Surtos de Doenças/estatística & dados numéricos , Período de Incubação de Doenças Infecciosas , Vírus da Influenza A Subtipo H1N1/fisiologia , Influenza Humana/epidemiologia , Influenza Humana/transmissão , Havaí/epidemiologia , Humanos , Influenza Humana/virologia , Japão/epidemiologia , ProbabilidadeRESUMO
Various definitions of fitness are essentially based on the number of descendants of an allele or a phenotype after a sufficiently long time. However, these different definitions do not explicate the continuous evolution of life histories. Herein, we focus on the eigenfunction of an age-structured population model as fitness. The function generates an equation, called the Hamilton-Jacobi-Bellman equation, that achieves adaptive control of life history in terms of both the presence and absence of the density effect. Further, we introduce a perturbation method that applies the solution of this equation to the long-term logarithmic growth rate of a stochastic structured population model. We adopt this method to realize the adaptive control of heterogeneity for an optimal foraging problem in a variable environment as the analyzable example. The result indicates that the eigenfunction is involved in adaptive strategies under all the environments listed herein. Thus, we aim to systematize adaptive life histories in the presence of density effects and variable environments using the proposed objective function as a universal fitness candidate.
Assuntos
Modelos Teóricos , Heterogeneidade GenéticaRESUMO
In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status could be boosted if they have contact with infective agent. According to the idea of the Aron's malaria model, we incorporate a boosting mechanism expressed by reset of recovery-age (immunity clock) into the SIRS epidemic model. We established the mathematical well-posedness of our formulation and showed that the initial invasion condition and the endemicity can be characterized by the basic reproduction number $ R_0 $. Our focus is to investigate the condition to determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, because it is a crucial point for disease prevention strategy whether there exist subcritical endemic steady states. Based on a recent result by Martcheva and Inaba [1], we have determined the direction of bifurcation that endemic steady states bifurcate from the disease-free steady state when the basic reproduction number passes through the unity. Finally, we have given a necessary and sufficient condition for backward bifurcation to occur.
Assuntos
Doenças Transmissíveis , Epidemias , Malária , Número Básico de Reprodução , Doenças Transmissíveis/epidemiologia , Humanos , Malária/epidemiologia , Modelos BiológicosRESUMO
BACKGROUND: The pandemic coronavirus disease 2019 (COVID-19) has spread and caused enormous and serious damages to many countries worldwide. One of the most typical interventions is the social distancing such as lockdown that would contribute to reduce the number of contacts among undiagnosed individuals. However, prolongation of the period of such a restrictive intervention could hugely affect the social and economic systems, and the outbreak will come back if the strong social distancing policy will end earlier due to the economic damage. Therefore, the social distancing policy should be followed by massive testing accompanied with quarantine to eradicate the infection. METHODS: In this paper, we construct a mathematical model and discuss the effect of massive testing with quarantine, which would be less likely to affect the social and economic systems, and its efficacy has been proved in South Korea, Taiwan, Vietnam and Hong Kong. RESULTS: By numerical calculation, we show that the control reproduction number is monotone decreasing and convex downward with respect to the testing rate, which implies that the improvement of the testing rate would highly contribute to reduce the epidemic size if the original testing rate is small. Moreover, we show that the recurrence of the COVID-19 epidemic in Japan could be possible after the lifting of the state of emergency if there is no massive testing and quarantine. CONCLUSIONS: If we have entered into an explosive phase of the epidemic, the massive testing could be a strong tool to prevent the disease as long as the positively reacted individuals will be effectively quarantined, no matter whether the positive reaction is pseudo or not. Since total population could be seen as a superposition of smaller communities, we could understand how testing and quarantine policy might be powerful to control the disease.
RESUMO
Backward bifurcation is an important property of infectious disease models. A centre manifold method has been developed by Castillo-Chavez and Song for detecting the presence of backward bifurcation and deriving a necessary and sufficient condition for its occurrence in Ordinary Differential Equations (ODE) models. In this paper, we extend this method to partial differential equation systems. First, we state a main theorem. Next we illustrate the application of the new method on a chronological age-structured Susceptible-Infected-Susceptible (SIS) model with density-dependent recovery rate, an age-since-infection structured HIV/AIDS model with standard incidence and an age-since-infection structured cholera model with vaccination.
Assuntos
Envelhecimento/patologia , Modelos Biológicos , Fatores Etários , Cólera/epidemiologia , Suscetibilidade a Doenças/epidemiologia , Infecções por HIV/epidemiologia , HumanosRESUMO
In this paper, we investigate an SIRS epidemic model with chronological age structure in a demographic steady state. Although the age-structured SIRS model is a simple extension of the well-known age-structured SIR epidemic model, we have to develop new technique to deal with problems due to the reversion of susceptibility for recovered individuals. First we give a standard proof for the well-posedness of the normalized age-structured SIRS model. Next we examine existence of endemic steady states by fixed point arguments and bifurcation method, where we introduce the next generation operator and the basic reproduction number R0 to formulate endemic threshold results. Thirdly we investigate stability of steady states by the bifurcation calculation and the comparison method, and we show existence of a compact attractor and discuss the global behavior based on the population persistence theory. Finally we give some numerical examples and discuss the effect of mass-vaccination on R0 and the critical coverage of immunization based on the reinfection threshold.
Assuntos
Epidemias , Viroses/epidemiologia , Viroses/imunologia , Fatores Etários , Algoritmos , Número Básico de Reprodução , Coeficiente de Natalidade , Simulação por Computador , Fertilidade , Humanos , Sistema Imunitário , Imunidade , Imunização , Vacinação em Massa , Modelos Biológicos , Mortalidade , Dinâmica Populacional , RecidivaRESUMO
In this paper, we develop the theory of a state-reproduction number for a multistate class age structured epidemic system and apply it to examine the asymptomatic transmission model. We formulate a renewal integral equation system to describe the invasion of infectious diseases into a multistate class age structured host population. We define the state-reproduction number for a class age structured system, which is the net reproduction number of a specific host type and which plays an analogous role to the type-reproduction number [M.G. Roberts, J.A.P. Heesterbeek, A new method for estimating the effort required to control an infectious disease, Proc. R. Soc. Lond. B 270 (2003) 1359; J.A.P. Heesterbeek, M.G. Roberts, The type-reproduction number T in models for infectious disease control, Math. Biosci. 206 (2007) 3] in discussing the critical level of public health intervention. The renewal equation formulation permits computations not only of the state-reproduction number, but also of the generation time and the intrinsic growth rate of infectious diseases. Subsequently, the basic theory is applied to capture the dynamics of a directly transmitted disease within two types of infected populations, i.e., asymptomatic and symptomatic individuals, in which the symptomatic class is observable and hence a target host of the majority of interventions. The state-reproduction number of the symptomatic host is derived and expressed as a measurable quantity, leading to discussion on the critical level of case isolation. The serial interval and other epidemiologic indices are computed, clarifying the parameters on which these indices depend. As a practical example, we illustrate the eradication threshold for case isolation of smallpox. The generation time and serial interval are comparatively examined for pandemic influenza.
Assuntos
Surtos de Doenças/prevenção & controle , Influenza Humana/epidemiologia , Modelos Estatísticos , Varíola/epidemiologia , Humanos , Influenza Humana/transmissão , Saúde Pública/métodos , Varíola/transmissãoRESUMO
In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R(0) is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.
Assuntos
Surtos de Doenças , Infecções por HIV/epidemiologia , HIV/crescimento & desenvolvimento , Homossexualidade , Modelos Biológicos , Fatores Etários , Número Básico de Reprodução , Infecções por HIV/transmissão , Humanos , Masculino , Dinâmica Populacional , Comportamento SexualRESUMO
Among the four groups of HIV-1 (M, N, O, and P), HIV-1M alone is pandemic and has rapidly expanded across the world. However, why HIV-1M has caused a devastating pandemic while the other groups remain contained is unclear. Interestingly, only HIV-1M Vpu, a viral protein, can robustly counteract human tetherin, which tethers budding virions. Therefore, we hypothesize that this property of HIV-1M Vpu facilitates human-to-human viral transmission. Adopting a multilayered experimental-mathematical approach, we demonstrate that HIV-1M Vpu confers a 2.38-fold increase in the prevalence of HIV-1 transmission. When Vpu activity is lost, protected human populations emerge (i.e., intrinsic herd immunity develops) through the anti-viral effect of tetherin. We also reveal that all Vpus of transmitted/founder HIV-1M viruses maintain anti-tetherin activity. These findings indicate that tetherin plays the role of a host restriction factor, providing 'intrinsic herd immunity', whereas Vpu has evolved in HIV-1M as a tetherin antagonist.
Assuntos
Antígenos CD/metabolismo , Infecções por HIV/imunologia , Infecções por HIV/metabolismo , HIV-1/imunologia , Proteínas do Vírus da Imunodeficiência Humana/imunologia , Imunidade Coletiva , Proteínas Virais Reguladoras e Acessórias/imunologia , Algoritmos , Motivos de Aminoácidos , Linhagem Celular , Sequência Conservada , Proteínas Ligadas por GPI/metabolismo , Infecções por HIV/epidemiologia , Infecções por HIV/transmissão , Infecções por HIV/virologia , HIV-1/metabolismo , Proteínas do Vírus da Imunodeficiência Humana/química , Proteínas do Vírus da Imunodeficiência Humana/metabolismo , Humanos , Modelos Teóricos , Pandemias , Matrizes de Pontuação de Posição Específica , Ligação Proteica , Carga Viral , Proteínas Virais Reguladoras e Acessórias/química , Proteínas Virais Reguladoras e Acessórias/metabolismoRESUMO
Cell-to-cell viral infection, in which viruses spread through contact of infected cell with surrounding uninfected cells, has been considered as a critical mode of virus infection. However, since it is technically difficult to experimentally discriminate the two modes of viral infection, namely cell-free infection and cell-to-cell infection, the quantitative information that underlies cell-to-cell infection has yet to be elucidated, and its impact on virus spread remains unclear. To address this fundamental question in virology, we quantitatively analyzed the dynamics of cell-to-cell and cell-free human immunodeficiency virus type 1 (HIV-1) infections through experimental-mathematical investigation. Our analyses demonstrated that the cell-to-cell infection mode accounts for approximately 60% of viral infection, and this infection mode shortens the generation time of viruses by 0.9 times and increases the viral fitness by 3.9 times. Our results suggest that even a complete block of the cell-free infection would provide only a limited impact on HIV-1 spread.
Assuntos
Infecções por HIV/virologia , HIV-1/fisiologia , Internalização do Vírus , Liberação de Vírus , Humanos , Células Jurkat , Modelos TeóricosRESUMO
In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.