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1. Voluntary vaccination may not stop monkeypox outbreak: A game-theoretic model

   https://doi.org/10.1371/journal.pntd.0010970  

   Augsburger, Ian B.; Galanthay, Grace K.; Tarosky, Jacob H.; Rychtář, Jan; Taylor, Dewey (December 2022, PLOS Neglected Tropical Diseases)

   Carabali, Mabel (Ed.)

   Monkeypox (MPX) is a viral zoonotic disease that was endemic to Central and West Africa. However, during the first half of 2022, MPX spread to almost 60 countries all over the world. Smallpox vaccines are about 85% effective in preventing MPX infections. Our objective is to determine whether the vaccines should be mandated or whether voluntary use of the vaccine could be enough to stop the MPX outbreak. We incorporate a standard SVEIR compartmental model of MPX transmission into a game-theoretical framework. We study a vaccination game in which individuals decide whether or not to vaccinate by assessing their benefits and costs. We solve the game for Nash equilibria, i.e., the vaccination rates the individuals would likely adopt without any outside intervention. We show that, without vaccination, MPX can become endemic in previously non-endemic regions, including the United States. We also show that to “not vaccinate” is often an optimal solution from the individual’s perspective. Moreover, we demonstrate that, for some parameter values, there are multiple equilibria of the vaccination game, and they exhibit a backward bifurcation. Thus, without centrally mandated minimal vaccination rates, the population could easily revert to no vaccination scenario. 

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2. A Game-Theoretic Model of Voluntary Yellow Fever Vaccination to Prevent Urban Outbreaks

   https://doi.org/10.3390/g13040055  

   Caasi, Jovic Aaron; Joseph, Brian M.; Kodiyamplakkal, Heera J.; Manibusan, Jaelene Renae; Camacho Aquino, Leslie J.; Oh, Hyunju; Rychtář, Jan; Taylor, Dewey (August 2022, Games)

   Yellow fever is a vector-borne acute viral hemorrhagic disease. It is endemic in tropical areas of Africa and Latin America but demonstrated the potential for international spread during the 2016 outbreak in Luanda, Angola. Yellow fever can be prevented by vaccination, vector control, and avoiding mosquito bites. To account for human behavior in disease dynamics, we add a game-theoretic component to a recent compartmental model of yellow fever transmission. The self-interested individuals evaluate the risks of contracting yellow fever and choose to vaccinate or avoid the bites to minimize the overall costs. We find the Nash equilibria, the optimal levels of vaccination and bite protections if the individuals can decide on the use of only one of the prevention methods as well as when they can decide on the use of both of them. In the later case, we show that vaccination is the preferred method of protection from the individual standpoint and, in the Nash equilibrium, individuals use vaccination only. Our model predicts the vaccination coverage in Angola to be around 65%, which is in reasonable agreement with the empirical value of 68%. We also study whether voluntary prevention can lead to the elimination of the disease in endemic areas. We show that voluntary vaccination alone is not enough to mitigate the risks of outbreaks, suggesting that a mandatory vaccination policy is necessary. 

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3. Impact of a multi-pronged cholera intervention in an endemic setting

   https://doi.org/10.1101/2023.12.14.23299970  

   Blake, Alexandre; Walder, Adam; Hanks, Ephraim; Welo, Placide Okitayembo; Luquero, Francisco; Bompangue, Didier; Bharti, Nita (December 2023, medRxiv)

   Abstract Cholera is a bacterial water-borne diarrheal disease transmitted via the fecal-oral route that causes high morbidity in sub-Saharan Africa and Asia. It is preventable with vaccination, and Water, Sanitation, and Hygiene (WASH) improvements. However, the impact of vaccination in endemic settings remains unclear. Cholera is endemic in the city of Kalemie, on the shore of Lake Tanganyika, in the Democratic Republic of Congo, where both seasonal mobility and the lake, a potential environmental reservoir, may promote transmission. Kalemie received a vaccination campaign and WASH improvements in 2013-2016. We assessed the impact of this intervention to inform future control strategies in endemic settings. We fit compartmental models considering seasonal mobility and environmentally-based transmission. We estimated the number of cases the intervention avoided, and the relative contributions of the elements promoting local cholera transmission. We estimated the intervention avoided 5,259 cases (95% credible interval: 1,576.6-11,337.8) over 118 weeks. Transmission did not rely on seasonal mobility and was primarily environmentally-driven. Removing environmental exposure or contamination could control local transmission. Repeated environmental exposure could maintain high population immunity and decrease the impact of vaccination in similar endemic areas. Addressing environmental exposure and contamination should be the primary target of interventions in such settings. Author summaryCholera is a major global health concern that causes high morbidity. It is a bacterial water-borne disease that can be transmitted via the fecal-oral route or the ingestion of contaminated water. Hence, both population mobility and environmental exposure can promote cholera persistence. The primary tools to prevent cholera include vaccination and Water, Sanitation, and Hygiene (WASH) improvements. The effectiveness of these interventions is well understood in epidemic settings, but their impact in endemic settings is unclear. Achieving cholera elimination requires disentangling the contributors to transmission, specifically population mobility and aquatic reservoirs, and assessing the impact of interventions performed in endemic settings.This study focuses on Kalemie, a cholera endemic city in the Democratic Republic of Congo, on shore of a lake that serves as a potential environmental reservoir. It quantifies the short-term impact of an intervention that used targeted vaccination and WASH. The study shows that the impact of vaccination was dampened by very high background immunity due to constant environmental exposure. This suggests that WASH improvements should be the primary intervention in such settings despite the time- and resource-intensive nature of implementation. 

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4. Mathematical Analysis of an SIVRWS Model for Pertussis with Waning and Naturally Boosted Immunity

   https://doi.org/10.3390/sym14112288  

   Safan, Muntaser; Barley, Kamal; Elhaddad, Mohamed M.; Darwish, Mohamed A.; Saker, Samir H. (November 2022, Symmetry)

   This work aims mainly to study the controllability of pertussis infection in the presence of waning and natural booster of pertussis immunity and to study their impact on the overall dynamics and disease outcomes. Therefore, an SIVRWS (Susceptible-Infected-Vaccinated-Recovered-Waned-Susceptible) model for pertussis infection spread in a demographically stationary, homogeneous, and fully symmetric mixing population is introduced. The model has been mathematically analyzed, where both equilibrium and stability analyses have been established, and uniform persistence of the model has been shown. The conditions on model parameters that ensure effective control of the infection have been derived. The effects of the interplay between waning and boosting pertussis immunity by re-exposure to Bordetella pertussis and vaccination on the dynamics have been investigated. The analytical results have been numerically confirmed and explained. The analysis reveals that ignoring the natural booster of immunity overestimates the endemic prevalence of the infection. Moreover, ignoring the differential susceptibility between secondary and primary susceptible individuals overestimates the critical vaccination coverage required to eliminate the infection. Moreover, the shorter the period of immunity acquired by either vaccination or experiencing natural infection, the higher the reproduction number and the endemic prevalence of infection, and therefore, the higher the effort needed to eliminate the infection. 

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5. EFFECTS OF VACCINATION ON THE TRANSMISSION DYNAMICS OF COVID-19 IN DOUGHERTY COUNTY OF GEORGIA, USA

   https://doi.org/10.1142/S021833902250019X  

   PANTHA, BUDDHI; MOHAMMED-AWEL, JEMAL; VAIDYA, NAVEEN K. (September 2022, Journal of Biological Systems)

   Despite the significant progress in the development of vaccines, the COVID-19 pandemic still poses difficulty for its control because of many obstacles such as the proper implementation of vaccination, public hesitancy towards vaccines, dropping out from the second dose, and varying level of protection after the first and the second doses. In this study, we develop a novel mathematical model of COVID-19 transmission, including two separate vaccinated compartments (first dose and both doses). We parametrize and validate our model using data from Dougherty county of Georgia, USA, one of the most affected counties, where the transmission trend clearly is associated with various policies and public events. We analyze our model for stability of equilibria and persistence of the disease, and formulate expression for reproduction numbers. We estimate that the basic reproduction number in Dougherty county is 1.69, and the effective reproduction number during the study period ranges from 0.26 to 6.36. The number of daily undiagnosed cases peaked at 310 per day, resulting in the maximum number of active infectious individuals to be 2471. Our model predicts that in a high transmission scenario, the vaccination strategies should be combined with other non-pharmaceutical prevention strategies to ensure transmission control. Moreover, our results emphasize that completing both doses of vaccines on time is critical to achieve maximum benefits from the vaccination programs. 

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