scholarly journals TRANSMISSION DYNAMICS OF DENGUE IN COSTA RICA: THE ROLE OF HOSPITALIZATIONS

2019 ◽  
Vol 27 (1) ◽  
pp. 241-266
Author(s):  
FABIO SANCHEZ ◽  
JORGE ARROYO-ESQUIVEL ◽  
PAOLA VÁSQUEZ
Keyword(s):  
Costa Rica ◽  
Compartmental Model ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Specific Parameter ◽  
Public Health Officials ◽  
Disease Free

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals in the transmission dynamics of dengue in Costa Rica. The basic reproductive number, R0, is computed, as well as a sensitivity analysis on R0 parameters. The global stability of the disease-free equilibrium is established. Numerical simulations under specific parameter scenarios are performed to determine optimal prevention/control strategies.

scholarly journals Mathematical modelling for malaria under resistance and population movement

2020 ◽  
Vol 38 (2) ◽  
pp. 133-163
Author(s):  
Cristhian Montoya ◽  
Jhoana P. Romero Leiton
Keyword(s):  
Human Population ◽  
Control Strategies ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Transmission Dynamic ◽  
Equilibrium Solutions ◽  
Population Movements ◽  
Existence And Stability ◽  
Theoretical Results ◽  
Disease Free

In this work, two mathematical models for malaria under resistance are presented. More precisely, the first model shows the interaction between humans and mosquitoes inside a patch under infection of malaria when the human population is resistant to antimalarial drug and mosquitoes population is resistant to insecticides. For the second model, human–mosquitoes population movements in two patches is analyzed under the same malaria transmission dynamic established in a patch. For a single patch, existence and stability conditions for the equilibrium solutions in terms of the local basic reproductive number are developed. These results reveal the existence of a forward bifurcation and the global stability of disease–free equilibrium. In the case of two patches, a theoretical and numerical framework on sensitivity analysis of parameters is presented. After that, the use of antimalarial drugs and insecticides are incorporated as control strategies and an optimal control problem is formulated. Numerical experiments are carried out in both models to show the feasibility of our theoretical results.

MODELING THE SCHISTOSOMIASIS ON THE ISLETS IN NANJING

2012 ◽  
Vol 05 (04) ◽  
pp. 1250037 ◽  
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.

TWO DYNAMIC MODELS ABOUT RABIES BETWEEN DOGS AND HUMAN

2008 ◽  
Vol 16 (04) ◽  
pp. 519-529 ◽  
Author(s):  
XIAOWEI WANG ◽  
JIE LOU
Keyword(s):  
Global Stability ◽  
Rural Areas ◽  
Theoretical Basis ◽  
Dynamic Models ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Ode Model ◽  
Disease Free ◽  
Rabies Vaccination

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.

scholarly journals Two new compartmental epidemiological models and their equilibria

2021 ◽  
Author(s):  
Jonas Balisacan ◽  
Monique Chyba ◽  
Corey Shanbrom
Keyword(s):  
Compartmental Model ◽  
Herd Immunity ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Epidemiology ◽  
Epidemiological Models ◽  
Classical Models ◽  
Asymptomatic Individuals ◽  
The Stability ◽  
Disease Free

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. Furthermore, the rise of new disease variants and the imperfection of vaccines suggest that concept of endemic equilibrium is perhaps more pertinent than that of herd immunity. Here we propose a new compartmental epidemiological model and study its equilibria, characterizing the stability of both the endemic and disease-free equilibria in terms of the basic reproductive number. Moreover, we introduce a second compartmental model, generalizing our first, which accounts for vaccinated individuals, and begin an analysis of its equilibria.

scholarly journals Model the transmission dynamics of COVID-19 propagation with public health intervention

2020 ◽  
Author(s):  
Dejen Ketema Mamo
Keyword(s):  
Public Health ◽  
Equilibrium Points ◽  
Public Health Intervention ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
High Coverage ◽  
Spread Model ◽  
Disease Free ◽  
At Home

AbstractIn this work, a researcher develop SHEIQRD (Susceptible-Stay at home-Exposed-Infected-Quarantine-Recovery-Death) coronavirus pandemic spread model. The disease-free and endemic equilibrium points are calculated and analyzed. The basic reproductive number ℛ0 is derived and its sensitivity analysis is done. COVID-19 pandemic spread is die out when ℛ0 ≤ 1 and its persist in the community whenever ℛ0 > 1. Efficient stay at home rate, high coverage of precise identification and isolation of expose and infected individuals, and redaction of transmission and stay at home return rate can be mitigate the pandemics. Finally, theoretical analysis and numerical results are consistent.

MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF SCHISTOSOMIASIS IN THE HUMAN-SNAIL HOSTS

2009 ◽  
Vol 17 (03) ◽  
pp. 397-423 ◽  
Author(s):  
EDWARD T. CHIYAKA ◽  
WINSTON GARIRA
Keyword(s):  
Center Manifold ◽  
Control Strategies ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Center Manifold Theory ◽  
Numerical Techniques ◽  
Manifold Theory ◽  
Host Parasite

The spread and persistence of schistosomiasis are some of the more complex host parasite processes to model mathematically because of the different larval forms assumed by the parasite and the requirement of two hosts during the life cycle. We construct a deterministic mathematical model to study the transmission dynamics of schistosomiasis where the miracidia and cercariae dynamics are incorporated. The model is analyzed to gain insights into the qualitative features of the equilibrium which allows the determination of the basic reproductive number. Conditions for existence of the endemic equilibrium are discussed and its local stability is determined using the Center Manifold Theory. Analytical and numerical techniques are employed to assess the conditions of containment and persistence of schistosomiasis. Our results show that control strategies that target the transmission of the disease from the snail to man will be more effective in the control of the disease than those that block the transmission from man to snail.

scholarly journals Effect of Rainfall for the Dynamical Transmission Model of the Dengue Disease in Thailand

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Pratchaya Chanprasopchai ◽  
Puntani Pongsumpun ◽  
I. Ming Tang
Keyword(s):  
Equilibrium State ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
Dengue Disease ◽  
The Stability ◽  
Disease Free ◽  
Endemic Equilibrium State ◽  
Stability Of The Solution

The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is analyzed. It is investigated by using the Routh-Hurwitz criteria. We find two equilibrium states: a disease-free state and an endemic equilibrium state. The basic reproductive number (R0) is obtained, which indicates the stability of each equilibrium state. Numerical results taking into account the rainfall are obtained and they are seen to correspond to the analytical results.

scholarly journals Modelling and Optimal Control of Typhoid Fever Disease with Cost-Effective Strategies

2017 ◽  
Vol 2017 ◽  
pp. 1-16 ◽  
Author(s):  
Getachew Teshome Tilahun ◽  
Oluwole Daniel Makinde ◽  
David Malonza
Keyword(s):  
Optimal Control ◽  
Typhoid Fever ◽  
Control Strategies ◽  
Cost Effective ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Effective Strategies ◽  
Next Generation Matrix ◽  
The Cost ◽  
Disease Free

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

MODELING THE IMPACT OF VOLUNTARY TESTING AND TREATMENT ON TUBERCULOSIS TRANSMISSION DYNAMICS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250029 ◽  
Author(s):  
S. MUSHAYABASA ◽  
C. P. BHUNU
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Positive Impact ◽  
Transmission Dynamics ◽  
Effective Control ◽  
Reproductive Number ◽  
Voluntary Testing ◽  
Manifold Theory ◽  
The Impact ◽  
Disease Free

A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemiological threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuberculosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.

scholarly journals Mathematical Analysis and Stochastic Stability of Nonlinear Epidemic Model with Incidence Rate

2020 ◽  
pp. 8-19
Author(s):  
Laid Chahrazed
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Saturated Incidence Rate ◽  
Saturated Incidence ◽  
The Stability ◽  
Disease Free ◽  
Temporary Immunity

In this work, we consider a nonlinear epidemic model with temporary immunity and saturated incidence rate. Size N(t) at time t, is divided into three sub classes, with N(t)=S(t)+I(t)+Q(t); where S(t), I(t) and Q(t) denote the sizes of the population susceptible to disease, infectious and quarantine members with the possibility of infection through temporary immunity, respectively. We have made the following contributions: The local stabilities of the infection-free equilibrium and endemic equilibrium are; analyzed, respectively. The stability of a disease-free equilibrium and the existence of other nontrivial equilibria can be determine by the ratio called the basic reproductive number, This paper study the reduce model with replace S with N, which does not have non-trivial periodic orbits with conditions. The endemic -disease point is globally asymptotically stable if R0 ˃1; and study some proprieties of equilibrium with theorems under some conditions. Finally the stochastic stabilities with the proof of some theorems. In this work, we have used the different references cited in different studies and especially the writing of the non-linear epidemic mathematical model with [1-7]. We have used the other references for the study the different stability and other sections with [8-26]; and sometimes the previous references.

Sign in / Sign up

Export Citation Format

Share Document