The Theory of Basic Reproduction Ratios

Zhao, Xiao-Qiang

doi:10.1007/978-3-319-56433-3_11

Cited by 8 publications

(2 citation statements)

References 48 publications

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“…It is not easy to find this number for more complex transmissions of a disease. There are some good and rigorous literature studies regarding this concept, such as Diekmann and Heesterbeek [47], Diekmann et al [48,49], Van den Driessche and Watmough [50], and Zhao [51], that provide a more systematic way of constructing the basic reproduction number. We prove, by standard theory, that T 0 mentioned above are indeed the basic reproduction number.…”

Section: The Basic Reproduction Number and Stability Of Thementioning

confidence: 99%

A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

Supriatna,

Napitupulu,

Ndii

et al. 2023

Computational and Mathematical Methods in Medicine

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In this paper, we present a mathematical model for the transmission of hantavirus among rodents and its effect on the number of hantavirus-infected human population. We investigate the model and present a standard analysis in mathematical epidemiology, such as determining the equilibria of the system and their stability analysis, together with the relationship to the basic reproduction number. It is found that the endemic equilibrium exists and is locally asymptotically stable when the basic reproduction number is greater than one; otherwise, the disease-free equilibrium is stable. Later on, we also show that by constructing a suitable Lyapunov function, the endemic equilibrium is globally asymptotically stable whenever it exists. Based on the basic reproduction number, we present a critical level of intervention to control the spread of the disease to humans. We found a significant finding from the present model that if the basic reproduction number is greater than one, then it is impossible to completely eliminate hantavirus disease in the system by solely focusing on any intervention for humans, like vaccination and curative action, without paying any attention to interventions for rodent populations. However, we can still decrease the density of infected humans with those interventions. Hence, we suggest that a combination of several interventions is needed to obtain effective control in eliminating the hantavirus. This information is useful for further study in finding an optimal control strategy to reduce or eliminate the transmission of hantavirus to humans.

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Section: The Basic Reproduction Number and Stability Of Thementioning

confidence: 99%

A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

Supriatna,

Napitupulu,

Ndii

et al. 2023

Computational and Mathematical Methods in Medicine

View full text Add to dashboard Cite

show abstract

“…It is not easy to find this number for more complex transmissions of a disease. There are some good and rigorous literature studies regarding this concept, such as [19,[22][23][24] and [25] (pp. 285-319), that provide a more systematic way of constructing the basic reproduction number.…”

Section: The Seir Continuous Model With Cpt Proportional To Infective...mentioning

confidence: 99%

SEIR Mathematical Model of Convalescent Plasma Transfusion to Reduce COVID-19 Disease Transmission

et al. 2021

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In some diseases, due to the restrictive availability of vaccines on the market (e.g., during the early emergence of a new disease that may cause a pandemic such as COVID-19), the use of plasma transfusion is among the available options for handling such a disease. In this study, we developed an SEIR mathematical model of disease transmission dynamics, considering the use of convalescent plasma transfusion (CPT). In this model, we assumed that the effect of CPT increases patient survival or, equivalently, leads to a reduction in the length of stay during an infectious period. We attempted to answer the question of what the effects are of different rates of CPT applications in decreasing the number of infectives at the population level. Herein, we analyzed the model using standard procedures in mathematical epidemiology, i.e., finding the trivial and non-trivial equilibrium points of the system including their stability and their relation to basic and effective reproduction numbers. We showed that, in general, the effects of the application of CPT resulted in a lower peak of infection cases and other epidemiological measures. As a consequence, in the presence of CPT, lowering the height of an infective peak can be regarded as an increase in the number of remaining healthy individuals; thus, the use of CPT may decrease the burden of COVID-19 transmission.

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Threshold Dynamics of a Temperature-Dependent Stage-Structured Mosquito Population Model with Nested Delays

Wang

Zou

2018

Bull Math Biol

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Mosquito-borne diseases remain a significant threat to public health and economics. Since mosquitoes are quite sensitive to temperature, global warming may not only worsen the disease transmission case in current endemic areas but also facilitate mosquito population together with pathogens to establish in new regions. Therefore, understanding mosquito population dynamics under the impact of temperature is considerably important for making disease control policies. In this paper, we develop a stage-structured mosquito population model in the environment of a temperature-controlled experiment. The model turns out to be a system of periodic delay differential equations with periodic delays. We show that the basic reproduction number is a threshold parameter which determines whether the mosquito population goes to extinction or remains persistent. We then estimate the parameter values for Aedes aegypti, the mosquito that transmits dengue virus. We verify the analytic result by numerical simulations with the temperature data of Colombo, Sri Lanka where a dengue outbreak occurred in 2017.

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The Theory of Basic Reproduction Ratios

Cited by 8 publications

References 48 publications

A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

A Mathematical Model for Transmission of Hantavirus among Rodents and Its Effect on the Number of Infected Humans

SEIR Mathematical Model of Convalescent Plasma Transfusion to Reduce COVID-19 Disease Transmission

Threshold Dynamics of a Temperature-Dependent Stage-Structured Mosquito Population Model with Nested Delays

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