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1. Optimal, near-optimal, and robust epidemic control

   https://doi.org/10.1038/s42005-021-00570-y  

   Morris, Dylan H.; Rossine, Fernando W.; Plotkin, Joshua B.; Levin, Simon A. (April 2021, Communications Physics)

   Abstract In the absence of drugs and vaccines, policymakers use non-pharmaceutical interventions such as social distancing to decrease rates of disease-causing contact, with the aim of reducing or delaying the epidemic peak. These measures carry social and economic costs, so societies may be unable to maintain them for more than a short period of time. Intervention policy design often relies on numerical simulations of epidemic models, but comparing policies and assessing their robustness demands clear principles that apply across strategies. Here we derive the theoretically optimal strategy for using a time-limited intervention to reduce the peak prevalence of a novel disease in the classic Susceptible-Infectious-Recovered epidemic model. We show that broad classes of easier-to-implement strategies can perform nearly as well as the theoretically optimal strategy. But neither the optimal strategy nor any of these near-optimal strategies is robust to implementation error: small errors in timing the intervention produce large increases in peak prevalence. Our results reveal fundamental principles of non-pharmaceutical disease control and expose their potential fragility. For robust control, an intervention must be strong, early, and ideally sustained. 

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2. Balancing mitigation strategies for viral outbreaks

   https://doi.org/10.3934/mbe.2024337  

   Karami, Hamed; Sanaei, Pejman; Smirnova, Alexandra (January 2024, Mathematical Biosciences and Engineering)

   Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the no control scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the reconstructed scenario, representing real-world data and interventions, (ⅲ) the social distancing control scenario covering a broad set of behavioral changes, (ⅳ) the vaccine control scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the both controls concurrently scenario incorporating social distancing and vaccine controls simultaneously. By comparing these scenarios, we provided a comprehensive analysis of various intervention strategies, offering valuable insights into disease dynamics. Our innovative approach to modeling the cost of control gave rise to a robust computational algorithm for solving optimal control problems associated with different public health regulations. Numerical results were supported by real data for the Delta variant of the COVID-19 pandemic in the United States. 

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3. The effects of seasonal human mobility and Aedes aegypti habitat suitability on Zika virus epidemic severity in Colombia

   https://doi.org/10.1371/journal.pntd.0012571  

   Lieberthal, Brandon; Allan, Brian; De_Urioste-Stone, Sandra; Mackay, Andrew; Soliman, Aiman; Wang, Shaowen; Gardner, Allison M (November 2024, PLOS Neglected Tropical Diseases)

   Morrison, Amy C (Ed.)

   The Zika virus epidemic of 2015–16, which caused over 1 million confirmed or suspected human cases in the Caribbean and Latin America, was driven by a combination of movement of infected humans and availability of suitable habitat for mosquito species that are key disease vectors. Both human mobility and mosquito vector abundances vary seasonally, and the goal of our research was to analyze the interacting effects of disease vector densities and human movement across metapopulations on disease transmission intensity and the probability of super-spreader events. Our research uses the novel approach of combining geographical modeling of mosquito presence with network modeling of human mobility to offer a comprehensive simulation environment for Zika virus epidemics that considers a substantial number of spatial and temporal factors compared to the literature. Specifically, we tested the hypotheses that 1) regions with the highest probability of mosquito presence will have more super-spreader events during dry months, when mosquitoes are predicted to be more abundant, 2) regions reliant on tourism industries will have more super-spreader events during wet months, when they are more likely to contribute to network-level pathogen spread due to increased travel. We used the case study of Colombia, a country with a population of about 50 million people, with an annual calendar that can be partitioned into overlapping cycles of wet and dry seasons and peak tourism and off tourism seasons that drive distinct cyclical patterns of mosquito abundance and human movement. Our results show that whether the first infected human was introduced to the network during the wet versus dry season and during the tourism versus off tourism season profoundly affects the severity and trajectory of the epidemic. For example, Zika virus was first detected in Colombia in October of 2015. Had it originated in January, a dry season month with high rates of tourism, it likely could have infected up to 60% more individuals and up to 40% more super-spreader events may have occurred. In addition, popular tourism destinations such as Barranquilla and Cartagena have the highest risk of super-spreader events during the winter, whereas densely populated areas such as Medellín and Bogotá are at higher risk of sustained transmission during dry months in the summer. Our research demonstrates that public health planning and response to vector-borne disease outbreaks requires a thorough understanding of how vector and host patterns vary due to seasonality in environmental conditions and human mobility dynamics. This research also has strong implications for tourism policy and the potential response strategies in case of an emergent epidemic. 

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4. Inter-provincial disparity of COVID-19 transmission and control in Nepal

   https://doi.org/10.1038/s41598-021-92253-5  

   Pantha, Buddhi; Acharya, Subas; Joshi, Hem Raj; Vaidya, Naveen K. (December 2021, Scientific Reports)

   null (Ed.)

   Abstract Despite the global efforts to mitigate the ongoing COVID-19 pandemic, the disease transmission and the effective controls still remain uncertain as the outcome of the epidemic varies from place to place. In this regard, the province-wise data from Nepal provides a unique opportunity to study the effective control strategies. This is because (a) some provinces of Nepal share an open-border with India, resulting in a significantly high inflow of COVID-19 cases from India; (b) despite the inflow of a considerable number of cases, the local spread was quite controlled until mid-June of 2020, presumably due to control policies implemented; and (c) the relaxation of policies caused a rapid surge of the COVID-19 cases, providing a multi-phasic trend of disease dynamics. In this study, we used this unique data set to explore the inter-provincial disparities of the important indicators, such as epidemic trend, epidemic growth rate, and reproduction numbers. Furthermore, we extended our analysis to identify prevention and control policies that are effective in altering these indicators. Our analysis identified a noticeable inter-province variation in the epidemic trend (3 per day to 104 per day linear increase during third surge period), the median daily growth rate (1 to 4% per day exponential growth), the basic reproduction number (0.71 to 1.21), and the effective reproduction number (maximum values ranging from 1.20 to 2.86). Importantly, results from our modeling show that the type and number of control strategies that are effective in altering the indicators vary among provinces, underscoring the need for province-focused strategies along with the national-level strategy in order to ensure the control of a local spread. 

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5. Optimal control of an epidemic model with treatment in the presence of media coverage

   https://doi.org/10.1016/j.sciaf.2024.e02138  

   Diagne, Mamadou L; Agusto, Folashade B; Rwezaura, Herieth; Tchuenche, Jean M; Lenhart, Suzanne (June 2024, Scientific African)

   During large scale outbreaks of infectious diseases, it is imperative that media report about the potential risks. Because media reporting plays a vital role in disseminating crucial information about diseases and its associated risk, understanding how media reports could influence individuals’ behavior and its potential impact on disease transmission dynamics is important. A mathematical model within an optimal control framework of a generic disease, accounting for treatment and media reporting of disease-induced deaths is formulated. Due to the complexity of choosing the best media function, our goal is to attempt to address the following research question: what is the effect of the media-induced functional response on mitigating the spread of the disease? Connecting the functional forms to the control problem is an approach that is not very developed in the literature. Thus, this study analyses the effect of different incidence functions on disease transmission, and the qualitative nature of epidemic dynamics by carrying out optimal control analysis using three different contact rates and a media function that is dependent on the number of deaths. Theoretical analyses show that the functional forms of the effective contact rate have no effect on initial disease transmission. Time-dependent controls for treatment and vaccination with a constant effective contact rate are incorporated to determine optimal control strategies. Numerical simulations show the short-term impact of media coverage on mitigating the spread of the disease, and it is observed that with three incidence functions used, the qualitative nature of the controls remains the same. The effective contact rates are graphically shown to have a population-level effect on the disease dynamics as the number of treated and recovered individuals could be significantly different. Finally, it is shown that treatment of infectives should be at its maximum rate for a longer period compared to vaccination, while concurrent implementation of vaccination and treatment is more impactful in mitigating the spread of the disease. Thus, it is imperative that media reports and health policy decision making on infectious diseases are contextualized. 

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