Modelling and optimal control of multi strain epidemics, with application to COVID-19.
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ABSTRACT:
SUBMITTER: Arruda EF
PROVIDER: S-EPMC8445490 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:This article considers the optimal control of the SIR model with both transmission and treatment uncertainty. It follows the model presented in Gatto and Schellhorn (2021). We make four significant improvements on the latter paper. First, we prove the existence of a solution to the model. Second, our interpretation of the control is more realistic: while in Gatto and Schellhorn (2021) the control α is the proportion of the population that takes a basic dose of treatment, so that α>1 occurs only if some patients take more than a basic dose, in our paper, α is constrained between zero and one, and represents thus the proportion of the population undergoing treatment. Third, we provide a complete solution for the moderate infection regime (with constant treatment). Finally, we give a thorough interpretation of the control in the moderate infection regime, while Gatto and Schellhorn (2021) focused on the interpretation of the low infection regime. Finally, we compare the efficiency of our control to curb the COVID-19 epidemic to other types of control.
| S-EPMC8675184 | biostudies-literature
Project description:BackgroundThe health impact of COVID-19 may differ in African settings as compared to countries in Europe or China due to demographic, epidemiological, environmental and socio-economic factors. We evaluated strategies to reduce SARS-CoV-2 burden in African countries, so as to support decisions that balance minimising mortality, protecting health services and safeguarding livelihoods.MethodsWe used a Susceptible-Exposed-Infectious-Recovered mathematical model, stratified by age, to predict the evolution of COVID-19 epidemics in three countries representing a range of age distributions in Africa (from oldest to youngest average age: Mauritius, Nigeria and Niger), under various effectiveness assumptions for combinations of different non-pharmaceutical interventions: self-isolation of symptomatic people, physical distancing and 'shielding' (physical isolation) of the high-risk population. We adapted model parameters to better represent uncertainty about what might be expected in African populations, in particular by shifting the distribution of severity risk towards younger ages and increasing the case-fatality ratio. We also present sensitivity analyses for key model parameters subject to uncertainty.ResultsWe predicted median symptomatic attack rates over the first 12 months of 23% (Niger) to 42% (Mauritius), peaking at 2-4 months, if epidemics were unmitigated. Self-isolation while symptomatic had a maximum impact of about 30% on reducing severe cases, while the impact of physical distancing varied widely depending on percent contact reduction and R0. The effect of shielding high-risk people, e.g. by rehousing them in physical isolation, was sensitive mainly to residual contact with low-risk people, and to a lesser extent to contact among shielded individuals. Mitigation strategies incorporating self-isolation of symptomatic individuals, moderate physical distancing and high uptake of shielding reduced predicted peak bed demand and mortality by around 50%. Lockdowns delayed epidemics by about 3 months. Estimates were sensitive to differences in age-specific social mixing patterns, as published in the literature, and assumptions on transmissibility, infectiousness of asymptomatic cases and risk of severe disease or death by age.ConclusionsIn African settings, as elsewhere, current evidence suggests large COVID-19 epidemics are expected. However, African countries have fewer means to suppress transmission and manage cases. We found that self-isolation of symptomatic persons and general physical distancing are unlikely to avert very large epidemics, unless distancing takes the form of stringent lockdown measures. However, both interventions help to mitigate the epidemic. Shielding of high-risk individuals can reduce health service demand and, even more markedly, mortality if it features high uptake and low contact of shielded and unshielded people, with no increase in contact among shielded people. Strategies combining self-isolation, moderate physical distancing and shielding could achieve substantial reductions in mortality in African countries. Temporary lockdowns, where socioeconomically acceptable, can help gain crucial time for planning and expanding health service capacity.
| S-EPMC7553800 | biostudies-literature
Project description:Coronavirus disease 2019 (COVID-19) is a disease caused by severe acute respiratory syndrome coronavirus 2 (SARS CoV-2). It was declared on March 11, 2020, by the World Health Organization as pandemic disease. The disease has neither approved medicine nor vaccine and has made governments and scholars search for drastic measures in combating the pandemic. Regrettably, the spread of the virus and mortality due to COVID-19 has continued to increase daily. Hence, it is imperative to control the spread of the disease particularly using nonpharmacological strategies such as quarantine, isolation, and public health education. This work studied the effect of these different control strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contributions in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number and effective reproduction numbers were computed with and without interventions, respectively, and were used to carry out the sensitivity analysis that identified the critical parameters contributing to the spread of COVID-19. The optimal control analysis was carried out using the Pontryagin's maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings of the optimal control analysis and numerical simulations revealed that time-dependent interventions reduced the number of exposed and infected individuals compared to time-independent interventions. These interventions were time-bound and best implemented within the first 100 days of the outbreak. Again, the combined implementation of only two of these interventions produced a good result in reducing infection in the population. While, the combined implementation of all three interventions performed better, even though zero infection was not achieved in the population. This implied that multiple interventions need to be deployed early in order to reduce the virus to the barest minimum.
| S-EPMC7499329 | biostudies-literature
Project description:Background and objectiveThe outbreak of the current pandemic begun from the first individual of a 55-year old from Hubei province in China, the disease instigated by the new coronavirus spreading across the world. Scientists presently speculate this coronavirus, SARS-CoV-2, originated in a bat and by one way or another jumped to another creature, potentially the pangolin, which at that point gave it to people. The ailment is currently spreading between individuals with no animal delegate. Researchers are struggling to follow the infection back to where it started to become familiar with its spread. In the event that, for example, specialists can locate the soonest cases, they might have the option to distinguish the creature have where the infection hides. In March and April 2020, researchers detailed that this virus created normally. Coronavirus has been become of the serious global phenomena in the recent years and has negative effects in the entire world health and economy. The virus is believed to have been associated with a host animal which human contracted. Subsequently, human-to-human infection began. Through migration as humans have become complex with easy mobility the disease has traveled to the entire continent. Now, numerous scientist are going on in the hope of obtaining medication and vaccination to prevent the spread of the disease and mortality of the disease. It is important that we obtain quantitative and qualitative information about the etiology of this disease which is crucial. Mathematical modeling is capable of providing qualitative information on many parameters that guides the decision making of health practitioners. In this work we focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions (NPIs). To find the role of factors/parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model.MethodsTo find the role of parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model. On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control mode. With the help of Hamiltonian and Lagrangian we minimize the density of contaminated stuff and infected human population.ResultsWe focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions(NPIs). On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control model. The major NPIs are, STAY HOME, SANITIZER (wash hands), EARLY CASE DETECTION (PCR Test) and FACE MASK. These NPIs helps in mitigation and reducing the size of outbreak of the disease.ConclusionWe check the existence of the optimal solution for the system. At the end, Using matlab we produce numerical simulations for validation of results of control variables. The results demonstrate that if there is no control (variables/interventios), 900 out 1000 susceptible individuals may be infected (exposed) in very short period. As such a circumstances no agency fighting against COVID-19 could be successful due to its limited resources.
| S-EPMC7339477 | biostudies-literature
Project description:ObjectiveThe COVID-19 pandemic forced colorectal cancer (CRC) screening programs to downscale their colonoscopy capacity. In this study, we assessed strategies to deal with temporary restricted colonoscopy capacity in a FIT-based CRC screening program while aiming to retain the maximum possible preventive effect of the screening program.DesignWe simulated the Dutch national CRC screening program inviting individuals between ages 55 and 75 for biennial FIT using the MISCAN-Colon model including the 3-month disruption in the first half of 2020 due to the COVID-19 pandemic. For the second half of 2020 and 2021, we simulated three different strategies for the total target population: 1) increasing the FIT cut-off, 2) skipping one screening for specific screening ages, and 3) extending the screening interval. We estimated the impact on required colonoscopy capacity in 2020-2021 and life years (LYs) lost in the long-term.ResultsIncreasing the FIT cut-off, skipping screening ages and extending the screening interval resulted in a maximum reduction of 25,100 (-17.0%), 16,100(-10.9%) and 19,000 (-12.9%) colonoscopies, respectively. Modelling an increased FIT cut-off, the number of LYs lost ranged between 1,400 and 4,400. Skipping just a single screening age resulted in approximately 2,700 LYs lost and this was doubled in case of skipping two screening ages. Extending the screening interval up to 34 months had the smallest impact on LYs lost (up to 1,100 LYs lost).ConclusionThis modelling study shows that to anticipate on restricted colonoscopy capacity, temporarily extending the screening interval retains the maximum possible preventive effect of the CRC screening program.
| S-EPMC9231802 | biostudies-literature
Project description:Epicentres are the focus of COVID-19 research, whereas emerging regions with mainly imported cases due to population movement are often neglected. Classical compartmental models are useful, however, likely oversimplify the complexity when studying epidemics. This study aimed to develop a multi-regional, hierarchical-tier mathematical model for better understanding the complexity and heterogeneity of COVID-19 spread and control. By incorporating the epidemiological and population flow data, we have successfully constructed a multi-regional, hierarchical-tier SLIHR model. With this model, we revealed insight into how COVID-19 was spread from the epicentre Wuhan to other regions in Mainland China based on the large population flow network data. By comprehensive analysis of the effects of different control measures, we identified that Level 1 emergency response, community prevention and application of big data tools significantly correlate with the effectiveness of local epidemic containment across different provinces of China outside the epicentre. In conclusion, our multi-regional, hierarchical-tier SLIHR model revealed insight into how COVID-19 spread from the epicentre Wuhan to other regions of China, and the subsequent control of local epidemics. These findings bear important implications for many other countries and regions to better understand and respond to their local epidemics associated with the ongoing COVID-19 pandemic.
| S-EPMC8014041 | biostudies-literature
Project description:In this paper, we develop a mathematical model for the spread and control of the coronavirus disease. An outbreak of COVID-19 has led to more than one million confirmed cases as of April 3rd, 2020. Understanding the early spread dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe COVID-19 spread with four datasets from within and outside of Wuhan, China; it is estimated how spread in Wuhan varied between January and February 2020. It is used these estimates to assess the potential for sustained human-to-human spread to occur in locations outside Wuhan if disease holders were introduced. It is combined SEIR framework model with data on cases of COVID-19 in China and International cases that originated in Wuhan to estimate how spread had varied over time during January and February 2020. Based on these estimates, it is calculated the probability that freshly introduced cases might produce outbreaks in other regions. Also, it is calculated approximately the median day by day basic reproduction number in Wuhan, refused from 2·45 (95% CI: 1·16-4·87) one week before travel restrictions were introduced on Jan 23rd, 2020, to 1.05 (0·42-2·40) one week after. Based on our estimates of, presumptuous SARS approximating disparity, it is computed that in locations with a similar spread potential to Wuhan in near the beginning of January, some time ago there are at least four independently set up cases, there is a more than fifty percent chance the infection will found within those inhabitants. COVID-19 spreading probably refused in Wuhan during delayed January 2020, corresponding with the prologue of voyage control channels. As more cases arrive in international locations with similar spread potential to Wuhan, before these organize measures, it is likely many chains of spread will fail to create initially but might lead to innovative outbreaks ultimately.
| S-EPMC7441022 | biostudies-literature
Project description:BackgroundCOVID-19 has spread worldwide since its emergence in 2019. In contrast to many other countries with epidemics, Japan differed in that it avoided lockdowns and instead asked people for self-control. A travel campaign was conducted with a sizable budget, but the number of PCR tests was severely limited. These choices may have influenced the course of the epidemic.MethodsThe increase or decrease in the classes of SARS-CoV-2 variants was estimated by analyzing the published sequences with an objective multivariate analysis. This approach observes the samples in multiple directions, digesting complex differences into simpler forms. The results were compared over time with the number of confirmed cases, PCR tests, and overseas visitors. The kinetics of infection were analyzed using the logarithmic growth rate.ResultsThe declared states of emergency failed to alter the movement of the growth rate. Three epidemic peaks were caused by domestically mutated variants. In other countries, there are few cases in which multiple variants have peaked. However, due to the relaxation of immigration restrictions, several infective variants have been imported from abroad and are currently competing for expansion, creating the fourth peak. By April 2021, these foreign variants exceeded 80%. The chaotic situation in Japan will continue for some time, in part because no effort has been made to identify asymptomatic carriers, and details of the vaccination program are undecided.
| S-EPMC8483016 | biostudies-literature
Project description:The COVID-19 pandemic has forced societies across the world to resort to social distancing to slow the spread of the SARS-CoV-2 virus. Due to the economic impacts of social distancing, there is growing desire to relax these measures. To characterize a range of possible strategies for control and to understand their consequences, we performed an optimal control analysis of a mathematical model of SARS-CoV-2 transmission. Given that the pandemic is already underway and controls have already been initiated, we calibrated our model to data from the USA and focused our analysis on optimal controls from May 2020 through December 2021. We found that a major factor that differentiates strategies that prioritize lives saved versus reduced time under control is how quickly control is relaxed once social distancing restrictions expire in May 2020. Strategies that maintain control at a high level until at least summer 2020 allow for tapering of control thereafter and minimal deaths, whereas strategies that relax control in the short term lead to fewer options for control later and a higher likelihood of exceeding hospital capacity. Our results also highlight that the potential scope for controlling COVID-19 until a vaccine is available depends on epidemiological parameters about which there is still considerable uncertainty, including the basic reproduction number and the effectiveness of social distancing. In light of those uncertainties, our results do not constitute a quantitative forecast and instead provide a qualitative portrayal of possible outcomes from alternative approaches to control.
| S-EPMC7473596 | biostudies-literature
Project description:The coronavirus disease (COVID-19) has infected more than 79 million individuals, with 1.7 million deaths worldwide. Several countries have implemented social distancing and testing policies with contact tracing as a measure to flatten the curve of the ongoing pandemic. Optimizing these control measures is urgent given the substantial societal and economic impacts associated with infection and interventions. To determine the optimal social distancing and testing strategies, we developed a mathematical model of COVID-19 transmission and applied optimal control theory, identifying the best approach to reduce the epidemiological burden of COVID-19 at a minimal cost. The results demonstrate that testing as a standalone optimal strategy does not have a significant effect on the final size of an epidemic, but it would delay the peak of the pandemic. If social distancing is the sole control strategy, it would be optimal to gradually increase the level of social distancing as the incidence curve of COVID-19 grows, and relax the measures after the curve has reached its peak. Compared with a single strategy, combined social distancing and testing strategies are demonstrated to be more efficient at reducing the disease burden, and they can delay the peak of the disease. To optimize these strategies, testing should be maintained at a maximum level in the early phases and after the peak of the epidemic, whereas social distancing should be intensified when the prevalence of the disease is greater than 15%. Accordingly, public health agencies should implement early testing and switch to social distancing when the incidence level begins to increase. After the peak of the pandemic, it would be optimal to gradually relax social distancing and switch back to testing.
| S-EPMC7772089 | biostudies-literature