Epidemic model formulation and analysis for diarrheal infections caused by salmonella

SIMULATION ◽  
2017 ◽  
Vol 93 (7) ◽  
pp. 543-552 ◽  
Author(s):  
Ojaswita Chaturvedi ◽  
Mandu Jeffrey ◽  
Edward Lungu ◽  
Shedden Masupe
Keyword(s):  
Parameter Estimation ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Elementary Model ◽  
Partial Rank Correlation ◽  
Parameter Values ◽  
Working Out ◽  
Disease Free

Epidemic modeling can be used to gain better understanding of infectious diseases, such as diarrhea. In the presented research, a continuous mathematical model has been formulated for diarrhea caused by salmonella. This model has been analyzed and simulated to be established in a functioning form. Elementary model analysis, such as working out the disease-free state and basic reproduction number, has been done for this model. The basic reproduction number has been calculated using the next generation matrix method. Stability analysis of the model has been done using the Routh–Hurwitz method. Sensitivity analysis and parameter estimation have been completed for the system too using MATLAB packages that work on the Latin Hypercube Sampling and Partial Rank Correlation Coefficient methods. It was established that as long as R0 < 1, there will be no epidemic. Upon simulation using assumed parameter values, the results produced comprehended the epidemic theory and practical situations. The system was proven stable using the Routh–Hurwitz criterion and parameter estimation was successfully completed. Salmonella diarrhea has been successfully modeled and analyzed in this research. This model has been flexibly built and it can be integrated onto certain platforms to be used as a predictive system to prevent further infections of salmonella diarrhea.

scholarly journals Mathematical Modeling to Estimate the Reproductive Number and the Outbreak Size of COVID-19: The case of India and the World

2020 ◽  
Author(s):  
Durgesh Nandini Sinha
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Model Fitting ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Reproductive Number ◽  
Global Pandemic ◽  
The World ◽  
Partial Rank Correlation ◽  
Coefficient Method

Abstract Coronavirus disease (COVID-19) has become a global pandemic with more than 218,000 deaths in 211 different countries around the world. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus responsible for this deadliest disease. This paper describes a mathematical model for India, a country with the second highest population in the world with an extremely high population density of about 464 people per km2. This disease has multiphasic actions and reaction mode and our model SEIAQIm is based on six compartmental groups in the form of susceptible, exposed, infectious, asymptomatic, quarantine, and recovered immune factions. Latin Hypercube Sampling Partial Rank Correlation Coefficient method was used for the data analysis and model fitting. According to our model, India would reach its basic reproduction number R0=0.97 on May 14, 2020 with a total number of 73,800 estimated cases. Further, this study also equates the world's situation using the same model system and predicts by May 7, 2020 with a total number of 3,772,000 estimated confirmed cases. Moreover, the current mathematical model highlights the importance of social distancing as an effective method of containing spread of COVID-19.

scholarly journals A stochastic SEIHR model for COVID-19 data fluctuations

2021 ◽  
Author(s):  
Ruiwu Niu ◽  
Yin-Chi Chan ◽  
Eric W. M. Wong ◽  
Michaël Antonie van Wyk ◽  
Guanrong Chen
Keyword(s):  
Basic Reproduction Number ◽  
Stochastic Stability ◽  
Reproduction Number ◽  
General Trend ◽  
Sufficient Conditions ◽  
Compartmental Models ◽  
Threshold Behavior ◽  
Random Fluctuations ◽  
Parameter Values ◽  
Disease Free

Abstract Although deterministic compartmental models are useful for predicting the general trend of a disease's spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.

scholarly journals Assessing the risk of bluetongue to UK livestock: uncertainty and sensitivity analyses of a temperature-dependent model for the basic reproduction number

2007 ◽  
Vol 5 (20) ◽  
pp. 363-371 ◽  
Author(s):  
Simon Gubbins ◽  
Simon Carpenter ◽  
Matthew Baylis ◽  
James L.N Wood ◽  
Philip S Mellor
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Latin Hypercube Sampling ◽  
Sensitivity Analyses ◽  
Biting Rate ◽  
The Uk ◽  
Temperature Dependent Model ◽  
The Basic Reproduction Number

Since 1998 bluetongue virus (BTV), which causes bluetongue, a non-contagious, insect-borne infectious disease of ruminants, has expanded northwards in Europe in an unprecedented series of incursions, suggesting that there is a risk to the large and valuable British livestock industry. The basic reproduction number, R 0 , provides a powerful tool with which to assess the level of risk posed by a disease. In this paper, we compute R 0 for BTV in a population comprising two host species, cattle and sheep. Estimates for each parameter which influences R 0 were obtained from the published literature, using those applicable to the UK situation wherever possible. Moreover, explicit temperature dependence was included for those parameters for which it had been quantified. Uncertainty and sensitivity analyses based on Latin hypercube sampling and partial rank correlation coefficients identified temperature, the probability of transmission from host to vector and the vector to host ratio as being most important in determining the magnitude of R 0 . The importance of temperature reflects the fact that it influences many processes involved in the transmission of BTV and, in particular, the biting rate, the extrinsic incubation period and the vector mortality rate.

scholarly journals Optimal Control Strategies of HFMD in Wenzhou, China

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zuqin Ding ◽  
Yong Li ◽  
Yongli Cai ◽  
Yueping Dong ◽  
Weiming Wang
Keyword(s):  
Optimal Control ◽  
Reproduction Number ◽  
Control Strategies ◽  
Rank Correlation ◽  
Foot And Mouth Disease ◽  
Latin Hypercube Sampling ◽  
Chi Square ◽  
Course Of Disease ◽  
Contact Rates ◽  
Partial Rank Correlation

In this paper, we investigate the dynamics and optimal control strategies of a modified hand, foot, and mouth disease (HFMD) model incorporating the EV-A71 vaccination in Wenzhou, China, analytically and numerically. We define the basic reproduction number R0 and show that it can be used to determine whether HFMD becomes extinct or not. Based on the monthly reported HFMD cases in Wenzhou for 76 months, we estimate the parameters in the dynamic model by using the method of minimum chi-square fitting, conduct the sensitivity analysis to investigate the influence of each uncertain parameter on R0 with the methods of Latin hypercube sampling and partial rank correlation coefficient, and find that the EV-A71 vaccination does not lead to the extinction of HFMD, but slightly reduces the incidence of HFMD. In order to control the spread of HFMD in Wenzhou, we need to increase the rate of EV-A71 vaccination, decrease the contact rates, and shorten the course of disease.

scholarly journals Analysis of stability and sensitivity of deterministic and stochastic models for the spread of the new corona virus SARS-CоV-2

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 1045-1063
Author(s):  
Bojana Jovanovic ◽  
Jasmina Ðordjevic ◽  
Jelena Manojlovic ◽  
Nenad Suvak
Keyword(s):  
Sensitivity Analysis ◽  
Stochastic Model ◽  
Basic Reproduction Number ◽  
Stochastic Models ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Stochastic Version ◽  
Analysis Of Stability ◽  
Parameter Values ◽  
Disease Free

Basic reproduction number for deterministic SEIPHAR model and its stochastic counterpart for the spread of SARS-CoV-2 virus are analyzed and compared. For deterministic version of the model, conditions for stability of the disease-free equilibrium are derived and, in addition, conditions for existence of bifurcation state related to endemic equilibrium are established. For stochastic model, conditions for extinction and persistence in mean of the disease are derived. Complete sensitivity analysis of thresholds between the extinction and mean-persistence are performed for both the deterministic and the stochastic version of the model. Influence of variation in parameter values is illustrated for epidemics in Wuhan in early 2020.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Wang ◽  
Shujing Gao ◽  
Yueli Luo ◽  
Dehui Xie
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Logistic Growth ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free ◽  
The Basic Reproduction Number

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

scholarly journals Simple MSEIR Model for Measles Transmission

2019 ◽  
pp. 1-11
Author(s):  
Mojeeb Al-Rahman EL-Nor Osman ◽  
Appiagyei Ebenezer ◽  
Isaac Kwasi Adu
Keyword(s):  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Recovery Rate ◽  
Birth Rate ◽  
Reproduction Number ◽  
Progression Rate ◽  
Asymptotically Stable ◽  
The Stability ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an Immunity-Susceptible-Exposed-Infectious-Recovery (MSEIR) mathematical model was used to study the dynamics of measles transmission. We discussed that there exist a disease-free and an endemic equilibria. We also discussed the stability of both disease-free and endemic equilibria.  The basic reproduction number  is obtained. If , then the measles will spread and persist in the population. If , then the disease will die out.  The disease was locally asymptotically stable if  and unstable if  . ALSO, WE PROVED THE GLOBAL STABILITY FOR THE DISEASE-FREE EQUILIBRIUM USING LASSALLE'S INVARIANCE PRINCIPLE OF Lyaponuv function. Furthermore, the endemic equilibrium was locally asymptotically stable if , under certain conditions. Numerical simulations were conducted to confirm our analytic results. Our findings were that, increasing the birth rate of humans, decreasing the progression rate, increasing the recovery rate and reducing the infectious rate can be useful in controlling and combating the measles.

scholarly journals On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
Author(s):  
Malen Etxeberria-Etxaniz ◽  
Santiago Alonso-Quesada ◽  
Manuel De la Sen
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Impulsive Vaccination ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

scholarly journals Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 328 ◽  
Author(s):  
Yanli Ma ◽  
Jia-Bao Liu ◽  
Haixia Li
Keyword(s):  
Lyapunov Function ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

Sign in / Sign up

Export Citation Format

Share Document