scholarly journals Dynamics of Tuberculosis (TB) with Drug Resistance to First-Line Treatment and Leaky Vaccination: A Deterministic Modelling Perspective

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dominic Otoo ◽  
Shaibu Osman ◽  
Stephen Atta Poku ◽  
Elvis Kobina Donkoh
Keyword(s):  
Drug Resistance ◽  
Deterministic Model ◽  
Control Measure ◽  
Equilibrium Points ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
First Line ◽  
Susceptible Population ◽  
Deterministic Modelling

A deterministic model was formulated and employed in the analysis of the dynamics of tuberculosis with a keen emphasis on vaccination and drug resistance as the first line of treatment. It was assumed that some of the susceptible population were vaccinated but with temporal immunity. This is due to the fact that vaccines do not confer permanent immunity. Moreover, part of the infected individual after treatment grows resistance to the drug. Infective immigrants were also considered to be part of the population. The basic reproductive number for the model is estimated using the next-generation matrix method. The equilibrium points of the TB model and their local and global stability were determined. It was established that if the basic reproductive number was less than unity R 0 < 1 , then the disease free equilibrium is stable and unstable if R 0 > 1 . Furthermore, we investigated the optimal prevention, treatment, and vaccination as control measures for the disease. As the objective functional was optimised, there have been a significant reduction in the number of infections and an increase in the number of recovery. The best control measure in combating tuberculosis infections is prevention and vaccination of the susceptible population.

scholarly journals Modelling the Transmission Dynamics of Tuberculosis in the Ashanti Region of Ghana

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Felix Okoe Mettle ◽  
Prince Osei Affi ◽  
Clement Twumasi
Keyword(s):  
Deterministic Model ◽  
Equilibrium Points ◽  
Herd Immunity ◽  
Transmission Dynamics ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Seir Model ◽  
High Burden ◽  
Ashanti Region ◽  
Over Time

Mathematical models can aid in elucidating the spread of infectious disease dynamics within a given population over time. In an attempt to model tuberculosis (TB) dynamics among high-burden districts in the Ashanti Region of Ghana, the SEIR epidemic model with demography was employed within both deterministic and stochastic settings for comparison purposes. The deterministic model showed success in modelling TB infection in the region to the transmission dynamics of the stochastic SEIR model over time. It predicted tuberculosis dying out in ten of twelve high-burden districts in the Ashanti Region, but an outbreak in Obuasi municipal and Amansie West district. The effect of introducing treatment at the incubation stage of TB transmission was also investigated, and it was discovered that treatment introduced at the exposed stage decreased the spread of TB. Branching process approximation was used to derive explicit forms of relevant epidemiological quantities of the deterministic SEIR model for stability analysis of equilibrium points. Numerical simulations were performed to validate the overall infection rate, basic reproductive number, herd immunity threshold, and Malthusian parameter based on bootstrapping, jackknife, and Latin Hypercube sampling schemes. It was recommended that the Ghana Health Service should find a good mechanism to detect TB in the early stages of infection in the region. Public health attention must also be given to districts with a potentially higher risk of experiencing endemic TB even though the estimates of the overall epidemic thresholds from our SEIR model suggested that the Ashanti Region as a whole had herd immunity against TB infection.

scholarly journals Inferring epidemic containment probability from non-pharmaceutical interventions using a Gillespie-based epidemic model

2021 ◽  
Author(s):  
Yasuhiko Kawato ◽  
Masatoshi Yamasaki ◽  
Tomomasa Matsuyama ◽  
Tohru Mekata ◽  
Takafumi Ito ◽  
...  
Keyword(s):  
Stochastic Simulation ◽  
Epidemic Model ◽  
Deterministic Model ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Model Parameters ◽  
Gillespie Algorithm ◽  
Susceptible Population ◽  
Markovian Processes ◽  
Pharmaceutical Interventions

The Gillespie algorithm, which is a stochastic numerical simulation of continuous-time Markovian processes, has been proposed for simulating epidemic dynamics. In the present study, using the Gillespie-based epidemic model, we focused on each single trajectory by the stochastic simulation to infer the probability of controlling an epidemic by non-pharmaceutical interventions (NPIs). The single trajectory analysis by the stochastic simulation suggested that a few infected people sometimes dissipated spontaneously without spreading of infection. The outbreak probability was affected by basic reproductive number but not by infectious duration and susceptible population size.　A comparative analysis suggested that the mean trajectory by the stochastic simulation has equivalent dynamics to a conventional deterministic model in terms of epidemic forecasting. The probability of outbreak containment by NPIs was inferred by trajectories derived from 1000 Monte Carlo simulation trials using model parameters assuming COVID-19 epidemic. The model-based analysis indicated that complete containment of the disease could be achieved by short-duration NPIs if performed early after the import of infected individuals. Under the correctness of the model assumptions, analysis of each trajectory by Gillespie-based stochastic model would provide a unique and valuable output such as the probabilities of outbreak containment by NPIs.

scholarly journals On the Optimal Control of a Malware Propagation Model

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1518
Author(s):  
Jose Diamantino Hernández Guillén ◽  
Ángel Martín del Rey ◽  
Roberto Casado Vara
Keyword(s):  
Optimal Control ◽  
Control Measure ◽  
Propagation Model ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Security Measures ◽  
Epidemic Process ◽  
Malware Propagation ◽  
Prevention Measure

An important way considered to control malware epidemic processes is to take into account security measures that are associated to the systems of ordinary differential equations that governs the dynamics of such systems. We can observe two types of control measures: the analysis of the basic reproductive number and the study of control measure functions. The first one is taken at the beginning of the epidemic process and, therefore, we can consider this to be a prevention measure. The second one is taken during the epidemic process. In this work, we use the theory of optimal control that is associated to systems of ordinary equations in order to find a new function to control malware epidemic through time. Specifically, this approach is evaluate on a particular compartmental malware model that considers carrier devices.

scholarly journals Analysis of a mosquito life cycle model

2021 ◽  
Vol Volume 34 - 2020 - Special... ◽  
Author(s):  
Albert Kouchéré ◽  
Hamadjam Abboubakar ◽  
Irepran Damakoa
Keyword(s):  
Life Cycle ◽  
Sterile Insect Technique ◽  
Deterministic Model ◽  
Communicable Disease ◽  
Control Measures ◽  
Reproductive Number ◽  
Gonotrophic Cycle ◽  
Complete Life Cycle ◽  
Trivial Equilibrium ◽  
International Audience

International audience The gonotrophic cycle of mosquitoes conditions the frequency of mosquito-human contacts. The knowledge of this important phenomenon in the mosquito life cycle is a fundamental element in the epidemiological analysis of a communicable disease such as mosquito-borne diseases.In this work, we analyze a deterministic model of the complete life cycle of mosquitoes which takes into account the principal phases of female mosquitoes' gonotrophic cycle, and the Sterile Insect technique combined with the use of insecticide as control measures to fight the proliferation of mosquitoes. We compute the corresponding mosquito reproductive number N ∗ and prove the global asymptotic stability of trivial equilibrium. We prove that the model admits two non-trivial equilibria whenever N^{∗} is greater than another threshold, N_c, which the total number of sterile mosquitoes depends on. Numerical simulations, using mosquito parameters of the Aedes species, are carried out to illustrate our analytical results and permit to show that the strategy which consists in combining the sterile insect technique with adulticides, when it is well done, effectively combats the proliferation of mosquitoes.

Modeling and stability analysis of the spread of novel coronavirus disease COVID-19

2021 ◽  
pp. 2150035
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
D. Abraham Vianny ◽  
Mary Jacintha ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Fractional Order ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Transmission Model ◽  
Reproductive Number ◽  
Discrete Version ◽  
Novel Coronavirus

Towards the end of 2019, the world witnessed the outbreak of Severe Acute Respiratory Syndrome Coronavirus-2 (COVID-19), a new strain of coronavirus that was unidentified in humans previously. In this paper, a new fractional-order Susceptible–Exposed–Infected–Hospitalized–Recovered (SEIHR) model is formulated for COVID-19, where the population is infected due to human transmission. The fractional-order discrete version of the model is obtained by the process of discretization and the basic reproductive number is calculated with the next-generation matrix approach. All equilibrium points related to the disease transmission model are then computed. Further, sufficient conditions to investigate all possible equilibria of the model are established in terms of the basic reproduction number (local stability) and are supported with time series, phase portraits and bifurcation diagrams. Finally, numerical simulations are provided to demonstrate the theoretical findings.

scholarly journals Differential effects of intervention timing on COVID-19 spread in the United States

2020 ◽  
Vol 6 (49) ◽  
pp. eabd6370 ◽  
Author(s):  
Sen Pei ◽  
Sasikiran Kandula ◽  
Jeffrey Shaman
Keyword(s):  
United States ◽  
Disease Transmission ◽  
Human Mobility ◽  
The United States ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Transmission Model ◽  
Reproductive Number ◽  
Mobility Data ◽  
Nonpharmaceutical Interventions

Assessing the effects of early nonpharmaceutical interventions on coronavirus disease 2019 (COVID-19) spread is crucial for understanding and planning future control measures to combat the pandemic. We use observations of reported infections and deaths, human mobility data, and a metapopulation transmission model to quantify changes in disease transmission rates in U.S. counties from 15 March to 3 May 2020. We find that marked, asynchronous reductions of the basic reproductive number occurred throughout the United States in association with social distancing and other control measures. Counterfactual simulations indicate that, had these same measures been implemented 1 to 2 weeks earlier, substantial cases and deaths could have been averted and that delayed responses to future increased incidence will facilitate a stronger rebound of infections and death. Our findings underscore the importance of early intervention and aggressive control in combatting the COVID-19 pandemic.

scholarly journals Stability Analysis and Clinic Phenomenon Simulation of a Fractional-Order HBV Infection Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yongmei Su ◽  
Sinuo Liu ◽  
Shurui Song ◽  
Xiaoke Li ◽  
Yongan Ye
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Order Model ◽  
Infected Cells ◽  
Set Up ◽  
Hbv Model

In this paper, a fractional-order HBV model was set up based on standard mass action incidences and quasisteady assumption. The basic reproductive number R0 and the cytotoxic T lymphocytes’ immune-response reproductive number R1 were derived. There were three equilibrium points of the model, and stable analysis of each equilibrium point was given with corresponding hypothesis about R0 or R1. Some numerical simulations were also given based on HBeAg clinical data, and the simulation showed that there existed positive logarithmic correlation between the number of infected cells and HBeAg, which was consistent with the clinical facts. The simulation also showed that the clinical individual differences should be reflected by the fractional-order model.

La Gloria, Mexico: The possible origins and response of a worldwide H1N1 flu pandemic in 2009

2013 ◽  
Vol 8 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Sahar Hashmi, MD
Keyword(s):  
Extended Period ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Telephone Interviews ◽  
Mexican Community ◽  
Nonpharmaceutical Interventions ◽  
Google Search ◽  
The Relationship ◽  
H1n1 Flu

This article traces the spread and route of the H1N1 pandemic in 2009 from its possible origin in La Gloria to Mexico City. A lack of health control measures or nonpharmaceutical interventions (NPIs) in La Gloria accounts for the unprecedented high basic reproductive number (R0) in that town and a higher incidence of H1N1 flu in Mexico City.We analyzed data collected from Mexican news articles, the Healthmaps dataset, the Google search engine, and telephone interviews with Mexican community physicians and residents. Our article uses a simple Susceptible Infected and Recovered model based on the data collected, to show the relationship between the disease curve and the implementation of NPI use. As a result of this study, we conclude that, with strict government measures to control the disease over an extended period of time, it is possible that many hundreds or even thousands of lives might be saved in the future.

scholarly journals Sensitivity and mathematical model analysis on secondhand smoking tobacco

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Birliew Fekede ◽  
Benyam Mebrate
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Primary Case ◽  
Susceptible Population ◽  
Proposed Model ◽  
Relative Change ◽  
Well Posed ◽  
Mathematical Model Analysis

AbstractIn this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

scholarly journals Estimating the risk on outbreak spreading of 2019-nCoV in China using transportation data

2020 ◽  
Author(s):  
Hsiang-Yu Yuan ◽  
M. Pear Hossain ◽  
Mesfin Tsegaye ◽  
Xiaolin Zhu ◽  
Pengfei Jia ◽  
...  
Keyword(s):  
Arrival Time ◽  
Critical Time ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Mathematical Framework ◽  
Cumulative Number ◽  
Border Control ◽  
Imported Cases ◽  
Novel Virus

AbstractA novel corona virus (2019-nCoV) was identified in Wuhan, China and has been causing an unprecedented outbreak in China. The spread of this novel virus can eventually become an international emergency. During the early outbreak phase in Wuhan, one of the most important public health tasks is to prevent the spread of the virus to other cities. Therefore, full-scale border control measures to prevent the spread of virus have been discussed in many nearby countries. At the same time, lockdown in Wuhan cityu (border control from leaving out) has been imposed. The challenge is that many people have traveled from Wuhan to other cities before the border control. Thus, it is difficult to forecast the number of imported cases at different cities and estimate their risk on outbreak emergence.Here, we have developed a mathematical framework incorporating city-to-city connections to calculate the number of imported cases of the novel virus from an outbreak source, and the cumulative number of secondary cases generated by the imported cases. We used this number to estimate the arrival time of outbreak emergence using air travel frequency data from Wuhan to other cities, collected from the International Air Transport Association database. In addition, a meta-population compartmental model was built based on a classical SIR approach to simulate outbreaks at different cities.We consider the scenarios under three basic reproductive number (R0) settings using the best knowledge of the current findings, from high (2.92), mild (1.68), to a much lower numbers (1.4). The mean arrival time of outbreak spreading has been determined. Under the high R0, the critical time is 17.9 days after December 31, 2019 for outbreak spreading. Under the low R0, the critical time is between day 26.2 to day 35 after December 31, 2019. To make an extra 30 days gain, under the low R0 (1.4), the control measures have to reduce 87% of the connections between the source and target cities. Under the higher R0 (2.92), the effect on reducing the chance of outbreak emergence is generally low until the border control measure was enhanced to reduce more than 95% of the connections.

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