Dynamic Transmission Model Research Articles

Dynamic model of respiratory infectious disease transmission by population mobility based on city network.

In modern societies, newly emerging infectious diseases spread rapidly between regions owing to frequent contact between people, causing considerable social and economic impacts. In this study, first, a scale-free city network was established, and then the shortest path between any two nodes was determined. Second, the movement path of tourists was designed based on the shortest path. Subsequently, every infected person's information, such as the city, infection time, onset and hospitalization, was confirmed based on their movement path. Third, the features of the transmission path and time distribution of the epidemic were characterized after summarizing the information. Finally, the reliability of the model was verified. The number of citizens and tourists in every city remained stable during this time. The results indicated that a larger basic reproduction number (R 0) and population outflow rate signify a faster growth rate of infected people in each city in the network. Compared with small and medium-sized cities, the epidemic spread faster in central cities. Population mobility was the decisive factor causing the spread of the epidemic to other areas. Therefore, the rapid spread of epidemics can be prevented by swiftly reducing the flow of people between cities.

Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination

COVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ω is suspended (Ω=0) is globally asymptotically stable when the effective reproduction number R0c<1 and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment (Ω>0), the endemic equilibrium using the centre manifold theory is shown to be stable globally whenever R0c>1. The model is extended into optimal control system and analyzed analytically using Pontryagin's Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.

The health and economic impact of switching vaccines in universal varicella vaccination programs using a dynamic transmission model: An Israel case study

ABSTRACT Currently available health economic models for varicella infection are designed to inform the cost-effectiveness of universal varicella vaccination (UVV) compared with no vaccination. However, in countries with an existing UVV program, these models cannot be used to evaluate whether to continue with the current varicella vaccine or to switch to an alternative vaccine. We developed a dynamic transmission model that incorporates the historical vaccination program to project the health and economic impact of changing vaccination strategies. We applied the model to Israel, which initiated UVV in 2008 with a quadrivalent vaccine, MMRV-GSK, and switched to MMRV-MSD in 2016. The model was calibrated to pre-vaccination incidence data before projecting the impact of the historical and future alternative vaccination strategies on the clinical burden of varicella. Total costs and QALYs lost due to varicella infections were projected to compare continuing with MMRV-MSD versus switching to MMRV-GSK in 2022. Over a 50-year time horizon, continuing with MMRV-MSD reduced varicella incidence further by 64%, reaching 35 cases per 100,000 population by 2072, versus a 136% increase in incidence with MMRV-GSK. Continuing with MMRV-MSD reduced cumulative hospitalization and outpatient cases by 48% and 58% (vs. increase of 137% and 91% with MMRV-GSK), respectively. Continuing with MMRV-MSD resulted in 139 fewer QALYs lost with total cost savings of 3% compared with switching to MMRV-GSK, from the societal perspective. In Israel, maintaining the UVV strategy with MMRV-MSD versus switching to MMRV-GSK is projected to further reduce the burden of varicella and cost less from the societal perspective.

The resurgence risk of COVID-19 in China in the presence of immunity waning and ADE: A mathematical modelling study

The mass vaccination program has been actively promoted since the end of 2020. However, waning immunity, antibody-dependent enhancement (ADE), and increased transmissibility of variants make the herd immunity untenable and the implementation of dynamic zero-COVID policy challenging in China. To explore how long the vaccination program can prevent China at low resurgence risk, and how these factors affect the long-term trajectory of the COVID-19 epidemics, we developed a dynamic transmission model of COVID-19 incorporating vaccination and waning immunity, calibrated using the data of accumulative vaccine doses administered and the COVID-19 epidemic in 2020 in mainland China. The prediction suggests that the vaccination coverage with at least one dose reach 95.87%, and two doses reach 77.92% on 31 August 2021. However, despite the mass vaccination, randomly introducing infected cases in the post-vaccination period causes large outbreaks quickly with waning immunity, particularly for SARS-CoV-2 variants with higher transmissibility. The results showed that with the current vaccination program and 50% of the population wearing masks, mainland China can be protected at low resurgence risk until 8 January 2023. However, ADE and higher transmissibility for variants would significantly shorten the low-risk period by over 1 year. Furthermore, intermittent outbreaks can occur while the peak values of the subsequent outbreaks decrease, indicating that subsequent outbreaks boosted immunity in the population level, further indicating that follow-up vaccination programs can help mitigate or avoid the possible outbreaks. The findings revealed that the integrated effects of multiple factors: waning immunity, ADE, relaxed interventions, and higher variant transmissibility, make controlling COVID-19 challenging. We should prepare for a long struggle with COVID-19, and not entirely rely on the COVID-19 vaccine.

A dynamic transmission model to calculate vaccination coverage needed to control COVID-19 in Germany

Abstract Background Control of the 2019 coronavirus disease (COVID-19) pandemic in Germany and return to pre-pandemic behaviour can only be achieved through natural or vaccine-induced immunity. Sufficient vaccine capacity promotes interest in the necessary and feasible target vaccination coverage. Methods An age and risk group stratified SEIR transmission model was used to assess the impact of vaccination coverage ranging 65%-95% for 12-59-year-olds and 90%-95% for ≥ 60-year-olds on COVID-19 incidence and intensive care unit (ICU) utilization between 01.07.2021-31.03.2022. Separate implementation of licensed vaccines allows to consider different efficacies, delivery rates and age-specific national vaccination recommendations. The analysis was conducted under different assumptions about contact behaviour during summer, reduction of daily contacts with increasing number of cases, daily vaccination uptake and the dominant variant. Data from the COVIMO study (N = 3004, data collection: 17.05.-09.06.2021) were used to define the population percentage willing to be vaccinated. Results The COVIMO study indicates an achievable vaccination compliance rate of 83.9% among 12-59-year-olds and 94.8% among those ≥ 60-year-olds. Maximum incidence or ICU utilization during observation period decreases from 385 to 61 and 6220 to 2800, respectively, with an increase in vaccination coverage from 65% to 95% of 12-59-year-olds, 90% vaccination rate among ≥ 60-year-olds, compared to pre-pandemic reduced contact behaviour in summer and reduction of contacts as case numbers increase. Conclusions The vaccination campaign should be continued at high intensity until at least 85% of 12-59-year-olds or 90% of ≥ 60-year-olds are fully vaccinated against COVID-19. Based on the population's willingness to be vaccinated, this goal seemed feasible. Key messages • Mathematical modeling was used to determine an evidence-based target vaccination coverage of ≥ 85%. • Expertise in modeling should be further strengthened.

Sliding motion control of Echinococcosis transmission dynamics model

Hydatid disease is a chronic zoonotic parasitic disease caused by Echinococcus. This paper proposes and analyzes a mathematical model of Echinococcosis disease system with a piecewise control function concerning threshold policy. The model is represented the control measures being triggered once the total number of infected hosts and human reaches the tolerant level. Model solutions are able to approach either one real equilibrium or the pseudo-equilibrium, depending on the tolerant threshold. Our results suggest that in order to diminish the outbreak of Echinococcosis or lead the number of infecteds to an expected level, it requires not only adequate hospital resources and certain government interventions, but also a good threshold policy.

Modeling Dynamic Responses to COVID-19 Epidemics: A Case Study in Thailand.

Quantifying the effects of control measures during the emergence and recurrence of SARS-CoV-2 poses a challenge to understanding the dynamic responses in terms of effectiveness and the population’s reaction. This study aims to estimate and compare the non-pharmaceutical interventions applied in the first and second outbreaks of COVID-19 in Thailand. We formulated a dynamic model of transmission and control. For each outbreak, the time interval was divided into subintervals characterized by epidemic events. We used daily case report data to estimate the transmission rates, the quarantine rate, and its efficiency by the maximum likelihood method. The duration-specific control reproduction numbers were calculated. The model predicts that the reproduction number dropped by about 91% after the nationwide lockdown in the first wave. In the second wave, after a high number of cases had been reported, the reproduction number decreased to about 80% in the next phase, but the spread continued. The estimated value was below the threshold in the last phase. For both waves, successful control was mainly induced by decreased transmission rate, while the explicit quarantine measure showed less effectiveness. The relatively weak control measure estimated by the model may have implications for economic impact and the adaptation of people.

Dynamics modeling of gear transmissions with asymmetric load-dependent friction

This paper proposes a new concise mathematical model of gear transmission dynamics with asymmetric load-dependent friction. It is built only upon the rigid-contact mechanics and the Coulomb friction law, but provides a new theoretical perspective on dynamic and static characteristics of gear transmissions. The presented model is of the form of a differential–algebraic inclusion (DAI) characterized by some parameters, including input-side and output-side asymmetry coefficients. The presented model properly captures the static friction and even the non-backdrivability. It is applicable to different classes of transmissions, such as leadscrew transmissions, worm gear transmissions, and spur gear transmissions. The DAI representation is extended into a multi-dimensional representation for articulated rigid-body systems driven through joint transmissions. Moreover, simulation algorithms are derived through the implicit Euler discretization. Some simulation examples illustrate the capability of the presented simulation algorithm to reproduce load-dependent asymmetric frictional behaviors, which cannot be reproduced by conventional load-independent joint friction models.

On the mathematical modeling of schistosomiasis transmission dynamics with heterogeneous intermediate host

Schistosomiasis is a neglected disease affecting almost every region of the world, with its endemicity mainly experience in sub-Saharan Africa. It remains difficult to eradicate due to heterogeneity associated with its transmission mode. A mathematical model of Schistosomiasis integrating heterogeneous host transmission pathways is thus formulated and analyzed to investigate the impact of the disease in the human population. Mathematical analyses are presented, including establishing the existence and uniqueness of solutions, computation of the model equilibria, and the basic reproduction number (R0). Stability analyses of the model equilibrium states show that disease-free and endemic equilibrium points are locally and globally asymptotically stable whenever R0 &amp;lt; 1 and R0&amp;gt;1, respectively. Additionally, bifurcation analysis is carried out to establish the existence of a forward bifurcation around R0 = 1. Using Latin-hypercube sampling, global sensitivity analysis was performed to examine and investigate the most significant model parameters in R0 which drives the infection. The sensitivity analysis result indicates that the snail's natural death rate, cercariae, and miracidia decay rates are the most influential parameters. Furthermore, numerical simulations of the model were done to show time series plots, phase portraits, and 3-D representations of the model and also to visualize the impact of the most sensitive parameters on the disease dynamics. Our numerical findings suggest that reducing the snail population will directly reduce Schistosomiasis transmission within the human population and thus lead to its eradication.

Projected Impact of Expanded Long-Acting Injectable PrEP Use Among Men Who Have Sex With Men on Local HIV Epidemics.

Pre-exposure prophylaxis (PrEP) is a key component in helping to reduce HIV incidence in the United States. Long-acting injectable (LAI) PrEP is a new alternative to oral PrEP; its potential to affect local HIV epidemics remains unclear. The Johns Hopkins HIV Economic Epidemiological model (JHEEM) is a dynamic model of HIV transmission in 32 US urban areas. We used JHEEM to project the HIV incidence among men who have sex with men (MSM) from 2020 to 2030 under a range of interventions aimed at increasing PrEP use. In the absence of any intervention (ie, current levels of oral PrEP and HIV care engagement), we projected a 19% reduction (95% credible interval, CrI 1% to 36%) in HIV incidence among MSM from 2020 to 2030 across all 32 cities. Adding 10% LAI PrEP uptake (above a base case of all oral PrEP) reduced the incidence by 36% (95% CrI 23% to 50%) by year 2030. This effect varied between cities, ranging from 22% in Atlanta to 51% in San Francisco. At 25% additional LAI PrEP uptake, this incidence reduction increased to 54% (95% CrI 45% to 64%). Reductions in incidence after introducing LAI PrEP were driven primarily by increased uptake and sustained usage rather than increased efficacy. LAI PrEP has the potential to substantially reduce HIV incidence among MSM, particularly if it increases PrEP uptake and continued use beyond existing levels. Because potential effects vary by city, the effectiveness of expanding PrEP use is dependent on local dynamics.

Modelling cervical cancer elimination using single-visit screening and treatment strategies in the context of high HIV prevalence: estimates for KwaZulu-Natal, South Africa.

IntroductionIn settings with high HIV prevalence, cervical cancer incidence rates are up to six‐fold higher than the global average of 13.1 cases per 100,000 women‐years. To inform strategies for global cervical cancer elimination, we used a dynamic transmission model to evaluate scalable screening and treatment strategies, accounting for HIV‐associated cancer risks and weighing prevention gains against overtreatment.MethodsWe developed a dynamic model of HIV‐HPV co‐infection and disease progression, which we calibrated to KwaZulu‐Natal, South Africa. Our baseline scenario reflects the current practice of HPV vaccination with a multi‐visit screening and treatment strategy involving cytology and colposcopy triage. We evaluated 13 comparator scenarios with increased vaccination coverage and one‐time, two‐time or repeat HIV‐targeted cervical cancer screening with the following single‐visit strategies: HPV DNA testing, HPV genotyping, automated visual evaluation (AVE) and HPV DNA with AVE triage. In all scenarios, HIV antiretroviral therapy, condom use and voluntary male medical circumcision continue at baseline levels. We simulated cancer incidence under each scenario from 2020 to 2120 using the 25 best‐fitting parameter sets. We present the median and range of model output from these simulations to account for parameter uncertainty.ResultsWe estimate that cervical cancer incidence will decrease by 87% with the continuation of current cervical cancer and HIV prevention strategies, from an age‐standardized rate per 100,000 women of 80.4 (range 58.2, 112.1) in 2020 to 10.7 (4.2, 29.9) in 2120. Scenarios scaling up vaccination and single‐visit strategies resulted in near‐ and long‐term gains. With repeat HIV‐targeted screening, incidence rates were projected to be 29–34% lower in 2030 relative to the baseline scenario, and elimination (incidence <4/100,000) was achieved with HPV DNA testing in 2095 and with AVE in 2114. A strategy of HPV DNA with AVE triage optimized the tradeoff between cancer cases averted and overtreatment.ConclusionsSingle‐visit screening strategies could avert a substantial burden of cervical cancer and accelerate progress towards elimination in settings with a high burden of HIV. Increasing the screening frequency among women with HIV and reducing loss‐to‐follow‐up for treatment will be key components of a successful elimination strategy.

Comparison of COVID-19 and seasonal influenza under different intensities of non-pharmaceutical interventions and vaccine effectiveness.

BackgroundThe COVID-19 pandemic has lasted more than 2 years, and the global epidemic prevention and control situation remains challenging. Scientific decision-making is of great significance to people's production and life as well as the effectiveness of epidemic prevention and control. Therefore, it is all the more important to explore its patterns and put forward countermeasures for the pandemic of respiratory infections.MethodsModeling of epidemiological characteristics was conducted based on COVID-19 and influenza characteristics using improved transmission dynamics models to simulate the number of COVID-19 and influenza infections in different scenarios in a hypothetical city of 100,000 people. By comparing the infections of COVID-19 and influenza in different scenarios, the impact of the effectiveness of vaccination and non-pharmaceutical interventions (NPIs) on disease trends can be calculated. We have divided the NPIs into three levels according to the degree of restriction on social activities (including entertainment venues, conventions, offices, restaurants, public transport, etc.), with social controls becoming progressively stricter from level 1 to level 3.ResultsIn the simulated scenario where susceptible individuals were vaccinated with three doses of COVID-19 coronaVac vaccine, the peak number of severe cases was 26.57% lower than that in the unvaccinated scenario, and the peak number of infection cases was reduced by 10.16%. In the scenario with level three NPIs, the peak number of severe cases was reduced by 7.79% and 15.43%, and the peak number of infection cases was reduced by 12.67% and 28.28%, respectively, compared with the scenarios with NPIs intensity of level 2 and level 1. For the influenza, the peak number of severe cases in the scenario where the entire population were vaccinated was 89.85%, lower than that in the unvaccinated scenario, and the peak number of infections dropped by 79.89%.ConclusionThe effectiveness of COVID-19 coronaVac vaccine for preventing severe outcomes is better than preventing infection; for the prevention and control of influenza, we recommend influenza vaccination as a priority over strict NPIs in the long term.

Distributed robust cooperative scheduling of multi-region integrated energy system considering dynamic characteristics of networks

Due to the advantages of reliability and economy, multiple adjacent region integrated energy systems (IESs) are interconnected to form a multi-region IES through multi-energy network. However, the limitation on private data exchange, multi-uncertainty and the complex dynamic characteristics bring challenges to the optimal scheduling of the multi-region IES. This paper proposes a distributed robust cooperative scheduling method for the multi-region electricity–natural gas–heat IES considering the dynamic characteristics and the uncertainties of wind turbine (WT) and electricity load. Firstly, a robust scheduling model of the multi-region IES considering dynamic characteristics and the uncertainties is built. In particular, the dynamic transmission models of gas and heating networks are constructed, and a regulation model of virtual heat storage is built to control the virtual heat storage in district heating network (DHN). Further, to preserve the information privacy and decision-making independence for each sub-region IES, a distributed cooperative scheduling framework based on the consensus-based alternating direction method of multipliers (ADMM) is developed for the multi-region IES, where the original robust scheduling model is decomposed into several subproblems that are solved independently. Moreover, the nonconvex dynamic natural gas flow function is addressed by convex relaxation technique, and the max–min robust model with binary variables is solved by alternative optimization procedure (AOP) method and duality theory. Finally, the simulation results show that the proposed method can converge reliably, realize the balance between the operation cost and the heat loss and provide a flexible scheduling scheme for the multi-region IES.

The Long-Term Clinical and Economic Impact of Universal Varicella Vaccination in Slovenia.

Background: Despite the substantial burden of varicella infection, Slovenia does not currently have a universal varicella vaccination (UVV) program. We modeled the long-term clinical and economic impact of implementing 2-dose UVV strategies compared with no vaccination in Slovenia. Methods: A previously published dynamic transmission model was adapted to the demographics, varicella seroprevalence, herpes zoster incidence, and contact patterns in Slovenia. Six 2-dose UVV strategies, vs no vaccination, were considered over a 50-year period, including monovalent vaccination (Varivax® [V-MSD] or Varilrix® [V-GSK]) at ages 12 and 24 months, or monovalent vaccination at 15 months followed by monovalent or quadrivalent vaccination (ProQuad® [MMRV-MSD] or Priorix- Tetra® [MMRV-GSK]) at 5.5 years. Costs, quality-adjusted life-years, and incremental cost-effectiveness ratios vs no vaccination were calculated to assess the economic impact of each strategy from payer and societal perspectives. Results: The incidence of varicella infection was estimated as 1228 per 100 000 population in the absence of UVV. Over 50 years, depending on vaccination strategy, UVV reduced varicella cases by 77% to 85% and was associated with substantial reductions in varicella deaths (39%-44%), outpatient cases (74%-82%), and hospitalizations (74%-82%). The greatest reductions were predicted with V-MSD (15 months/5.5 years) and V MSD/MMRV-MSD (15 months/5.5 years). Discussion: All 2-dose UVV strategies were cost-effective compared with no vaccination from payer and societal perspectives, with V-MSD (15 months/5.5 years) being the most favorable from both perspectives. Conclusion: Policymakers should consider implementing UVV to reduce the burden of varicella disease in Slovenia.

The Long-Term Clinical and Economic Impact of Universal Varicella Vaccination in Slovenia

Background: Despite the substantial burden of varicella infection, Slovenia does not currently have a universal varicella vaccination (UVV) program. We modeled the long-term clinical and economic impact of implementing 2-dose UVV strategies compared with no vaccination in Slovenia. Methods: A previously published dynamic transmission model was adapted to the demographics, varicella seroprevalence, herpes zoster incidence, and contact patterns in Slovenia. Six 2-dose UVV strategies, vs no vaccination, were considered over a 50-year period, including monovalent vaccination (Varivax® [V-MSD] or Varilrix® [V-GSK]) at ages 12 and 24 months, or monovalent vaccination at 15 months followed by monovalent or quadrivalent vaccination (ProQuad® [MMRV-MSD] or Priorix- Tetra® [MMRV-GSK]) at 5.5 years. Costs, quality-adjusted life-years, and incremental cost-effectiveness ratios vs no vaccination were calculated to assess the economic impact of each strategy from payer and societal perspectives. Results: The incidence of varicella infection was estimated as 1228 per 100 000 population in the absence of UVV. Over 50 years, depending on vaccination strategy, UVV reduced varicella cases by 77% to 85% and was associated with substantial reductions in varicella deaths (39%-44%), outpatient cases (74%-82%), and hospitalizations (74%-82%). The greatest reductions were predicted with V-MSD (15 months/5.5 years) and V MSD/MMRV-MSD (15 months/5.5 years). Discussion: All 2-dose UVV strategies were cost-effective compared with no vaccination from payer and societal perspectives, with V-MSD (15 months/5.5 years) being the most favorable from both perspectives. Conclusion: Policymakers should consider implementing UVV to reduce the burden of varicella disease in Slovenia.

Estimating the Economic and Clinical Value of Introducing Ceftazidime/Avibactam into Antimicrobial Practice in Japan: A Dynamic Modelling Study.

BackgroundAntimicrobial resistance (AMR) is one of the most serious public health challenges worldwide, including in Japan. Globally, research and development of new antimicrobials has stalled due to unfavorable market conditions, which undervalue antimicrobials. Furthermore, Japan faces the additional challenge of delayed commercialization for a number of recently approved treatments.ObjectiveThis study aims to examine the impact on AMR of introducing a new anti-infective treatment, ceftazidime/avibactam, into current treatment strategies. It reports the resulting clinical and economic outcomes from the perspective of healthcare payers in Japan.MethodsA previously published and validated dynamic disease transmission model was adapted to the Japanese setting. The model estimated health economic outcomes for treating three Gram-negative hospital-acquired infections, under different treatment strategies, from a healthcare payers’ perspective. Outcomes were assessed over a 10-year time horizon with a willingness-to-pay threshold of ¥5,000,000 (US$45,556) per quality-adjusted life-year (QALY) gained and an annual discount rate of 2% applied to costs and benefits.ResultsIntroducing ceftazidime/avibactam in the framework of a diversification strategy with piperacillin/tazobactam is associated with reducing 798,640 bed days, equating to ¥21.0 billion (US$190.9 million) savings in hospitalization costs, and a gain of 363,034 life-years, or 308,641 QALYs. This translates into a monetary benefit of ¥1.56 trillion (US$14.3 billion) to Japanese healthcare payers.DiscussionIntroducing a new antimicrobial agent into clinical practice is associated with considerable clinical and economic benefits. This analysis demonstrates that the approach taken to incorporate a new antimicrobial agent into clinical practice impacts on the scale of these clinical and economic benefits; greater benefits are associated with earlier use of antimicrobials as part of an antimicrobial stewardship program.ConclusionThis analysis shows that changing the way in which a new antimicrobial is used within a treatment strategy has the potential for additional significant clinical and economic value.Supplementary InformationThe online version contains supplementary material available at 10.1007/s41669-022-00368-w.

The Clinical and Economic Impact of a Nonavalent Versus Bivalent Human Papillomavirus National Vaccination Program in Taiwan

This study aimed to estimate the epidemiologic and economic impact of a nonavalent human papillomavirus (HPV) vaccination program for 13- to 14-year-old females compared with that of the bivalent vaccine in Taiwan. A previously developed dynamic transmission model for the nonavalent HPV vaccine was adapted to the Taiwan setting. The natural history of cervical cancer and genital warts was simulated by the HPV model assuming an 80% vaccination coverage rate in girls aged 13 to 14 years of age with a 2-dose schedule for the nonavalent and bivalent HPV vaccines. A lifetime duration of vaccine protection was assumed for the HPV vaccine types. The model estimated that the nonavalent HPV vaccine would prevent an additional 15 951 cervical cancer cases, 6600 cervical cancer-related deaths, 176 702 grade 2 or grade 3 cervical intraepithelial neoplasia cases, 103 959 grade 1 cervical intraepithelial neoplasia cases, and 1 115 317 genital warts cases compared with the bivalent HPV vaccine. The nonavalent HPV vaccination program was projected to cost an additional New Taiwan dollars (NTD) 675.21 per person and to produce an additional 0.00271 quality-adjusted life-year per person over 100 years compared with the bivalent HPV vaccine. Thus, the incremental cost-effectiveness ratio of the nonavalent HPV vaccine versus the bivalent HPV vaccine was NTD 249 462/quality-adjusted life-year. A nonavalent HPV vaccination program for 13- to 14-year-old girls would have additional public health and economic impacts and would be highly cost-effective compared with the bivalent HPV vaccine, relative to per capita gross domestic product, which is estimated at NTD 746 526 for Taiwan.

Research on the law of dynamic shifting and coordinated section shifting of tractor full-power shift transmission

With the rapid development of China’s agricultural economy, the domestic research on full-power shift transmissions is still immature. In view of the problem of poor transmission shift quality, this paper proposes a tractor full-power shift transmission shifting coordination section law. A transmission dynamics model based on Matlab/Simulink was simulated and analyzed. The results show that the quality of shifting only is better than that of only changing sections, and the quality of shifting after shifting first is worse than that of shifting after shifting first. And selected only the shift and first shift after the two laws of the section, the shortening of the clutch engagement time during the shift only, the impact degree is reduced over time, the first decrease is increased, and the sliding friction work is increased. The change of time between the shift and the transition period, the impact is reduced with time, and the sliding friction work is increased.

Optimal Control Solution for Rabies Disease Transmission within Free-ranging Dog

This paper considers deterministic model for transmission dynamics of rabies virus in the free-ranging dog population. The stability of system near by Disease Free Equilibrium point is analized using Next Generation Matrix. The effect of vaccination in susceptible dog population is considered on the model. We then present the effective reproduction number in the present of the vaccination. Further we developed the formula to obtain the optimal vaccination to eliminate the endemic equilibrium, via the Pontryagin Maximum Principle. Numerical example are presented to show the properties of the optimal control solution.

Epidemiological Characteristics and the Dynamic Transmission Model of Dengue Fever in Zhanjiang City, Guangdong Province in 2018.

Background: With the progress of urbanization, the mobility of people has gradually increased, which has led to the further spread of dengue fever. This study evaluated the transmissibility of dengue fever within districts and between different districts in Zhanjiang City to provide corresponding advice for cross-regional prevention and control. Methods: A mathematical model of transmission dynamics was developed to explore the transmissibility of the disease and to compare that between different regions. Results: A total of 467 DF cases (6.38 per 100,000 people) were reported in Zhanjiang City in 2018. In the model, without any intervention, the number of simulated cases in this epidemic reached about 950. The dengue fever transmissions between districts varied within and between regions. When the spread of dengue fever from Chikan Districts to other districts was cut off, the number of cases in other districts dropped significantly or even to zero. When the density of mosquitoes in Xiashan District was controlled, the dengue fever epidemic in Xiashan District was found to be significantly alleviated. Conclusions: When there is a dengue outbreak, timely measures can effectively control it from developing into an epidemic. Different prevention and control measures in different districts could efficiently reduce the risk of disease transmission.