Huanglongbing Model under the Control Strategy of Discontinuous Removal of Infected Trees

Our models characterize the transmission dynamics of rabies between human and dogs. Firstly, we build an ODE model to represent the natural spreading of rabies in dogs and human. We get the basic reproductive number R0 and the global stability for both the disease-free equilibrium and the endemic equilibrium. Then, we build a controlling model for rabies. We compare the efficiency of three strategies for controlling the rabies: culling, vaccination, culling and vaccination, and get controlling thresholds for different strategies. The results of analysis and simulations indicate that vaccination is the best choice and culling is the worst one to control rabies. Vaccination on dogs in cities and culling and vaccination on dogs in rural areas of China are recommended for controlling rabies. Our study provides a theoretical basis for controlling rabies in China.

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Infectious Disease infectious disease basic reproductive number Modeling infectious disease modeling

Encyclopedia of Sustainability Science and Technology ◽

10.1007/978-1-4419-0851-3_539 ◽

2012 ◽

pp. 5347-5357 ◽

Cited By ~ 1

Author(s):

Angela R. McLean

Keyword(s):

Infectious Disease ◽

Disease Modeling ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Infectious Disease Modeling

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Understanding the effect of temperature on Bluetongue disease risk in livestock

10.1101/759860 ◽

2019 ◽

Cited By ~ 1

Author(s):

Fadoua El Moustaid ◽

Zorian Thronton ◽

Hani Slamani ◽

Sadie J. Ryan ◽

Leah R. Johnson

Keyword(s):

Disease Risk ◽

Vector Competence ◽

Basic Reproductive Number ◽

Effect Of Temperature ◽

Reproductive Number ◽

Temperature Sensitive ◽

Modeling Tools ◽

Vector Borne Diseases ◽

Thermal Range ◽

Vector Borne

AbstractThe transmission of vector-borne diseases is governed by complex factors including pathogen characteristics, vector-host interactions, and environmental conditions. Temperature is a major driver for many vector-borne diseases including Bluetongue viral (BTV) disease, a midge-borne febrile disease of ruminants, notably livestock, whose etiology ranges from mild or asymptomatic to rapidly fatal, thus threatening animal agriculture and the economy of affected countries. Using modeling tools, we seek to predict where transmission can occur based on suitable temperatures for BTV. We fit thermal performance curves to temperature sensitive midge life history traits, using a Bayesian approach. Then, we incorporated these into a new formula for the disease basic reproductive number, R0, to include trait responses, for two species of key midge vectors, Culicoides sonorensis and Culicoides variipennis. Our results show that outbreaks of BTV are more likely between 15°C and 33°C with predicted peak transmission at 26°C. The greatest uncertainty in R0 is associated with the uncertainty in: mortality and fecundity of midges near optimal temperature for transmission; midges’ probability of becoming infectious post infection at the lower edge of the thermal range; and the biting rate together with vector competence at the higher edge of the thermal range. We compare our R0 to two other R0 formulations and show that incorporating thermal curves into all three leads to similar BTV risk predictions. To demonstrate the utility of this model approach, we created global suitability maps indicating the areas at high and long-term risk of BTV transmission, to assess risk, and anticipate potential locations of establishment.

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Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

Computational and Mathematical Methods in Medicine ◽

10.1155/2019/1352698 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Zhixing Hu ◽

Shanshan Yin ◽

Hui Wang

Keyword(s):

Hopf Bifurcation ◽

Infection Rate ◽

Disease Model ◽

Endemic Equilibrium ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Cure Rate ◽

Vector Borne Disease ◽

Vector Borne ◽

The Stability

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

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AN EPIDEMIOLOGICAL MODEL WITH MULTIPLE ENDEMIC STATES

Journal of Biological System ◽

10.1142/s0218339015400021 ◽

2015 ◽

Vol 23 (supp01) ◽

pp. S17-S31

Author(s):

GEISER VILLAVICENCIO-PULIDO ◽

IGNACIO BARRADAS ◽

LUNA BEATRIZ

Keyword(s):

Infectious Disease ◽

Backward Bifurcation ◽

Epidemiological Model ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Force Of Infection

We present a model describing the dynamics of an infectious disease for which the force of infection is diminished through a reaction of the susceptible to the number of infected individuals. We show that, even though the structure of the model is a simple one, different kinds of backward bifurcation can appear for values of the basic reproductive number bigger than one. Under some conditions on the parameters, multiple endemic equilibria may appear for values of the basic reproductive number less or greater than one.

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Global Stability for a Viral Infection Model with Saturated Incidence Rate

Abstract and Applied Analysis ◽

10.1155/2014/187897 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Huaqin Peng ◽

Zhiming Guo

Keyword(s):

Viral Infection ◽

Global Stability ◽

Incidence Rate ◽

Sufficient Conditions ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Infection Model ◽

Saturated Incidence Rate ◽

Saturated Incidence ◽

Viral Infection Model

A viral infection model with saturated incidence rate and viral infection with delay is derived and analyzed; the incidence rate is assumed to be a specific nonlinear formβxv/(1+αv). The existence and uniqueness of equilibrium are proved. The basic reproductive numberR0is given. The model is divided into two cases: with or without delay. In each case, by constructing Lyapunov functionals, necessary and sufficient conditions are given to ensure the global stability of the models.

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An artificially simulated outbreak of a respiratory infectious disease

10.21203/rs.2.14142/v7 ◽

2020 ◽

Author(s):

Zuiyuan Guo ◽

Shuang Xu ◽

Libo Tong ◽

Botao Dai ◽

Yuandong Liu ◽

...

Keyword(s):

Infectious Disease ◽

Infectious Diseases ◽

Attack Rate ◽

General Pattern ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Developmental Trend ◽

Collision Model ◽

Military Camp ◽

Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

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Predicting temperature-dependent transmission suitability of bluetongue virus in livestock

Parasites & Vectors ◽

10.1186/s13071-021-04826-y ◽

2021 ◽

Vol 14 (1) ◽

Author(s):

Fadoua El Moustaid ◽

Zorian Thornton ◽

Hani Slamani ◽

Sadie J. Ryan ◽

Leah R. Johnson

Keyword(s):

Vector Competence ◽

Transmission Risk ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Temperature Sensitive ◽

Temperature Dependent ◽

Modeling Tools ◽

Vector Borne Diseases ◽

Thermal Range ◽

Vector Borne

AbstractThe transmission of vector-borne diseases is governed by complex factors including pathogen characteristics, vector–host interactions, and environmental conditions. Temperature is a major driver for many vector-borne diseases including Bluetongue viral (BTV) disease, a midge-borne febrile disease of ruminants, notably livestock, whose etiology ranges from mild or asymptomatic to rapidly fatal, thus threatening animal agriculture and the economy of affected countries. Using modeling tools, we seek to predict where the transmission can occur based on suitable temperatures for BTV. We fit thermal performance curves to temperature-sensitive midge life-history traits, using a Bayesian approach. We incorporate these curves into S(T), a transmission suitability metric derived from the disease’s basic reproductive number, $$R_0.$$ R 0 . This suitability metric encompasses all components that are known to be temperature-dependent. We use trait responses for two species of key midge vectors, Culicoides sonorensis and Culicoides variipennis present in North America. Our results show that outbreaks of BTV are more likely between 15$$^{\circ }$$ ∘ C and $$34^{\circ }\hbox { C}$$ 34 ∘ C , with predicted peak transmission risk at 26 $$^\circ$$ ∘ C. The greatest uncertainty in S(T) is associated with the following: the uncertainty in mortality and fecundity of midges near optimal temperature for transmission; midges’ probability of becoming infectious post-infection at the lower edge of the thermal range; and the biting rate together with vector competence at the higher edge of the thermal range. We compare three model formulations and show that incorporating thermal curves into all three leads to similar BTV risk predictions. To demonstrate the utility of this modeling approach, we created global suitability maps indicating the areas at high and long-term risk of BTV transmission, to assess risk and to anticipate potential locations of disease establishment.

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An artificially simulated outbreak of a respiratory infectious disease

10.21203/rs.2.14142/v5 ◽

2020 ◽

Author(s):

Zuiyuan Guo ◽

Shuang Xu ◽

Libo Tong ◽

Botao Dai ◽

Yuandong Liu ◽

...

Keyword(s):

Infectious Disease ◽

Infectious Diseases ◽

Attack Rate ◽

General Pattern ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Developmental Trend ◽

Collision Model ◽

Military Camp ◽

Epidemiological Characteristics

Abstract Background Outbreaks of respiratory infectious diseases often occur in crowded places. To understand the pattern of spread of an outbreak of a respiratory infectious disease and provide a theoretical basis for targeted implementation of scientific prevention and control, we attempted to establish a stochastic model to simulate an outbreak of a respiratory infectious disease at a military camp. This model fits the general pattern of disease transmission and further enriches theories on the transmission dynamics of infectious diseases. Methods We established an enclosed system of 500 people exposed to adenovirus type 7 (ADV 7) in a military camp. During the infection period, the patients transmitted the virus randomly to susceptible people. The spread of the epidemic under militarized management mode was simulated using a computer model named “the random collision model”, and the effects of factors such as the basic reproductive number ( R 0 ), time of isolation of the patients (TOI), interval between onset and isolation (IOI), and immunization rates (IR) on the developmental trend of the epidemic were quantitatively analysed. Results Once the R 0 exceeded 1.5, the median attack rate increased sharply; when R 0 =3, with a delay in the TOI, the attack rate increased gradually and eventually remained stable. When the IOI exceeded 2.3 days, the median attack rate also increased dramatically. When the IR exceeded 0.5, the median attack rate approached zero. The median generation time was 8.26 days, (95% confidence interval [CI]: 7.84-8.69 days). The partial rank correlation coefficients between the attack rate of the epidemic and R 0 , TOI, IOI, and IR were 0.61, 0.17, 0.45, and -0.27, respectively. Conclusions The random collision model not only simulates how an epidemic spreads with superior precision but also allows greater flexibility in setting the activities of the exposure population and different types of infectious diseases, which is conducive to furthering exploration of the epidemiological characteristics of epidemic outbreaks.

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MODELING THE SCHISTOSOMIASIS ON THE ISLETS IN NANJING

International Journal of Biomathematics ◽

10.1142/s1793524511001799 ◽

2012 ◽

Vol 05 (04) ◽

pp. 1250037 ◽

Cited By ~ 5

Author(s):

LONGXING QI ◽

JING-AN CUI ◽

YUAN GAO ◽

HUAIPING ZHU

Keyword(s):

Differential Equations ◽

Global Stability ◽

Field Study ◽

Rattus Norvegicus ◽

Compartmental Model ◽

Endemic Equilibrium ◽

Basic Reproductive Number ◽

Reproductive Number ◽

Parasitic Diseases ◽

Disease Free

A compartmental model is established for schistosomiasis infection in Qianzhou and Zimuzhou, two islets in the center of Yangtzi River near Nanjing, P. R. China. The model consists of five differential equations about the susceptible and infected subpopulations of mammalian Rattus norvegicus and Oncomelania snails. We calculate the basic reproductive number R0 and discuss the global stability of the disease free equilibrium and the unique endemic equilibrium when it exists. The dynamics of the model can be characterized in terms of the basic reproductive number. The parameters in the model are estimated based on the data from the field study of the Nanjing Institute of Parasitic Diseases. Our analysis shows that in a natural isolated area where schistosomiasis is endemic, killing snails is more effective than killing Rattus norvegicus for the control of schistosomiasis.

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