Ebola could be eradicated through voluntary vaccination

Imperfect vaccine can yield multiple Nash equilibria in vaccination games

As infectious diseases continue to threaten communities across the globe, people are faced with a choice to vaccinate, or not. Many factors influence this decision, such as the cost of the disease, the chance of contracting the disease, the population vaccination coverage, and the efficacy of the vaccine. While the vaccination games in which individuals decide whether to vaccinate or not based on their own interests are gaining in popularity in recent years, the vaccine imperfection has been an overlooked aspect so far. In this paper we investigate the effects of an imperfect vaccine on the outcomes of a vaccination game. We use a simple SIR compartmental model for the underlying model of disease transmission. We model the vaccine imperfection by adding vaccination at birth and maintain a possibility for the vaccinated individual to become infected. We derive explicit conditions for the existence of different Nash equilibria, the solutions of the vaccination game. The outcomes of the game depend on the complex interplay between disease transmission dynamics (the basic reproduction number), the relative cost of the infection, and the vaccine efficacy. We show that for diseases with relatively low basic reproduction numbers (smaller than about 2.62), there is a little difference between outcomes for perfect or imperfect vaccines and thus the simpler models assuming perfect vaccines are good enough. However, when the basic reproduction number is above 2.62, then, unlike in the case of a perfect vaccine, there can be multiple equilibria. Moreover, unless there is a mandatory vaccination policy in place that would push the vaccination coverage above the value of unstable Nash equilibrium, the population could eventually slip to the "do not vaccinate" state. Thus, for diseases that have relatively high basic reproduction numbers, the potential for the vaccine not being perfect should be explicitly considered in the models.

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

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.

A game-theoretic model of rabies in domestic dogs with multiple voluntary preventive measures

Game theory is now routinely applied to quantitatively model the decision making of individuals presented with various voluntary actions that can prevent a given disease. Most models consider only a single preventive strategy and the case where multiple preventative actions are available is severely understudied. In our paper, we consider a very simple SI compartmental model of rabies in the domestic dog population. We study two choices of the dog owners: to vaccinate their dogs or to restrict the movements of unvaccinated dogs. We analyze the relatively rich patterns of Nash equilibria (NE). We show that there is always at least one NE at which the owners utilize only one form of prevention. However, there can be up to three different NEs at the same time: two NEs at which the owners use exclusively only the vaccination or movement restriction, and the third NE when the owners use both forms of prevention simultaneously. However, we also show that, unlike the first two types of NEs, the third kind of NE is not convergent stable.

A game-theoretic model of lymphatic filariasis prevention

Lymphatic filariasis (LF) is a mosquito-borne parasitic neglected tropical disease. In 2000, WHO launched the Global Programme to Eliminate Lymphatic Filariasis (GPELF) as a public health problem. In 2020, new goals for 2030 were set which includes a reduction to 0 of the total population requiring Mass Drug Administrations (MDA), a primary tool of GPELF. We develop a mathematical model to study what can happen at the end of MDA. We use a game-theoretic approach to assess the voluntary use of insect repellents in the prevention of the spread of LF through vector bites. Our results show that when individuals use what they perceive as optimal levels of protection, the LF incidence rates will become high. This is in striking difference to other vector-borne NTDs such as Chagas or zika. We conclude that the voluntary use of the protection alone will not be enough to keep LF eliminated as a public health problem and a more coordinated effort will be needed at the end of MDA.

Vaccination games in prevention of infectious diseases with application to COVID-19

Vaccination coverage is crucial for disease prevention and control. An appropriate combination of compulsory vaccination with voluntary vaccination is necessary to achieve the goal of herd immunity for some epidemic diseases such as measles and COVID-19. A mathematical model is proposed that incorporates both compulsory vaccination and voluntary vaccination, where a decision of voluntary vaccination is made on the basis of game evaluation by comparing the expected returns of different strategies. It is shown that the threshold of disease invasion is determined by the reproduction numbers, and an over-response in magnitude or information interval in the dynamic games could induce periodic oscillations from the Hopf bifurcation. The theoretical results are applied to COVID-19 to find out the strategies for protective immune barrier against virus variants.

EBOLA VIRUS DISEASE DYNAMICS WITH SOME PREVENTIVE MEASURES: A CASE STUDY OF THE 2018–2020 KIVU OUTBREAK

To fight against Ebola virus disease, several measures have been adopted. Among them, isolation, safe burial and vaccination occupy a prominent place. In this paper, we present a model which takes into account these three control strategies as well as the indirect transmission through a polluted environment. The asymptotic behavior of our model is achieved. Namely, we determine a threshold value [Formula: see text] of the control reproduction number [Formula: see text], below which the disease is eliminated in the long run. Whenever the value of [Formula: see text] ranges from [Formula: see text] and 1, we prove the existence of a backward bifurcation phenomenon, which corresponds to the case, where a locally asymptotically stable positive equilibrium co-exists with the disease-free equilibrium, which is also locally asymptotically stable. The existence of this bifurcation complicates the control of Ebola, since the requirement of [Formula: see text] below one, although necessary, is no longer sufficient for the elimination of Ebola, more efforts need to be deployed. When the value of [Formula: see text] is greater than one, we prove the existence of a unique endemic equilibrium, locally asymptotically stable. That is the disease may persist and become endemic. Numerically, we fit our model to the reported data for the 2018–2020 Kivu Ebola outbreak which occurred in Democratic Republic of Congo. Through the sensitivity analysis of the control reproduction number, we prove that the transmission rates of infected alive who are outside hospital are the most influential parameters. Numerically, we explore the usefulness of isolation, safe burial combined with vaccination and investigate the importance to combine the latter control strategies to the educational campaigns or/and case finding.

Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever

Zika fever is an emerging mosquito-borne disease. While it often causes no or only mild symptoms that are similar to dengue fever, Zika virus can spread from a pregnant woman to her baby and cause severe birth defects. There is no specific treatment or vaccine, but the disease can be mitigated by using several control strategies, generally focusing on the reduction in mosquitoes or mosquito bites. In this paper, we model Zika virus transmission and incorporate a game-theoretical approach to study a repeated population game of DEET usage to prevent insect bites. We show that the optimal use effectively leads to disease elimination. This result is robust and not significantly dependent on the cost of the insect repellents.

Mathematical analysis for the effect of voluntary vaccination on the propagation of Corona virus pandemic

In this manuscript, a new nonlinear model for the rapidly spreading Corona virus disease (COVID-19) is developed. We incorporate an additional class of vaccinated humans which ascertains the impact of vaccination strategy for susceptible humans. A complete mathematical analysis of this model is conducted to predict the dynamics of Corona virus in the population. The analysis proves the effectiveness of vaccination strategy employed and helps public health services to control or to reduce the burden of corona virus pandemic. We first prove the existence and uniqueness and then boundedness and positivity of solutions. Threshold parameter for the vaccination model is computed analytically. Stability of the proposed model at fixed points is investigated analytically with the help of threshold parameter to examine epidemiological relevance of the pandemic. We apply LaSalle's invariance principle from the theory of Lyapunov function to prove the global stability of both the equilibria. Two well known numerical techniques namely Runge-Kutta method of order 4 (RK4), and the Non-Standard Finite Difference (NSFD) method are employed to solve the system of ODE's and to validate our obtained theoretical results. For different coverage levels of voluntary vaccination, we explored a complete quantitative analysis of the model. To draw our conclusions, the effect of proposed vaccination on threshold parameter is studied numerically. It is claimed that Corona virus disease could be eradicated faster if a human community selfishly adopts mandatory vaccination measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effect of vaccination strategy on a disease dynamics.

Optimal Voluntary Vaccination of Adults and Adolescents Can Help Eradicate Hepatitis B in China

Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost.

Mathematical modelling of the use of insecticide-treated nets for elimination of visceral leishmaniasis in Bihar, India

Visceral leishmaniasis (VL) is a deadly neglected tropical disease caused by a parasite Leishmania donovani and spread by female sand flies Phlebotomus argentipes. There is conflicting evidence regarding the role of insecticide-treated nets (ITNs) on the prevention of VL. Numerous studies demonstrated the effectiveness of ITNs. However, KalaNet, a large trial in Nepal and India did not support those findings. The purpose of this paper is to gain insight into the situation by mathematical modelling. We expand a mathematical model of VL transmission based on the KalaNet trial and incorporate the use of ITNs explicitly into the model. One of the major contributions of this work is that we calibrate the model based on the available epidemiological data, generally independent of the KalaNet trial. We validate the model on data collected during the KalaNet trial. We conclude that in order to eliminate VL, the ITN usage would have to stay above 96%. This is higher than the 91% ITNs use at the end of the trial which may explain why the trial did not show a positive effect from ITNs. At the same time, our model indicates that asymptomatic individuals play a crucial role in VL transmission.

Optimal voluntary and mandatory insect repellent usage and emigration strategies to control the chikungunya outbreak on Reunion Island

In 2005, a chikungunya virus outbreak devastated the tropical island of Reunion, infecting a third of the total population. Motivated by the Reunion Island case study, we investigate the theoretic potential for two intervention measures under both voluntary and mandatory protocols to control a vector-borne disease when there is risk of the disease becoming endemic. The first measure uses insect repellent to prevent mosquito bites, while the second involves emigrating to the neighboring Mauritius Island to avoid infection. There is a threshold on the cost of using repellent above which both voluntary and mandatory regimes find it optimal to forgo usage. Below that threshold, mandatory usage protocols will eradicate the disease; however, voluntary adoption leaves the disease at a small endemic level. Emigrating from the island to avoid infection results in a tragedy-of-the-commons effect: while being potentially beneficial to specific susceptible individuals, the remaining islanders paradoxically face a higher risk of infection. Mandated relocation of susceptible individuals away from the epidemic is viable only if the cost of this relocation is several magnitudes lower than the cost of infection. Since this assumption is unlikely to hold for chikungunya, it is optimal to discourage such emigration for the benefit of the entire population. An underlying assumption about the conservation of human-vector encounter rates in mosquito biting behavior informs our conclusions and may warrant additional experimental verification.

A voluntary use of insecticide treated nets can stop the vector transmission of Chagas disease

One of the stated goals of the London Declaration on Neglected Tropical Diseases is the interruption of domiciliary transmissions of Chagas disease in the region of the Americas. We used a game-theoretic approach to assess the voluntary use of insecticide treated nets (ITNs) in the prevention of the spread of infection through vector bites. Our results show that individuals behave rationally and weigh the risks of insect bites against the cost of the ITNs. The optimal voluntary use of ITNs results in predicted incidence rates that closely track the real incidence rates in Latin America. This means that ITNs are effective and could be used to control the spread of the disease by relying on individual decisions rather than centralized policies. Our model shows that to completely eradicate the vector transmission through the voluntary individual use of ITNs, the cost of ITNs should be as low as possible.

High endemic levels of typhoid fever in rural areas of Ghana may stem from optimal voluntary vaccination behaviour

Typhoid fever has long established itself endemically in rural Ghana despite the availability of cheap and effective vaccines. We used a game-theoretic model to investigate whether the low vaccination coverage in Ghana could be attributed to rational human behaviour. We adopted a version of an epidemiological model of typhoid fever dynamics, which accounted not only for chronic life-long carriers but also for a short-cycle transmission in the immediate environment and a long-cycle transmission via contamination of the water supply. We calibrated the model parameters based on the known incidence data. We found that unless the (perceived) cost of vaccination is negligible, the individually optimal population vaccination rate falls significantly short of the societally optimal population vaccination rate needed to reach herd immunity. We expressed both the herd immunity and the optimal equilibrium vaccination rates in terms of only a few observable parameters such as the incidence rate, demographics, vaccine waning rate and the perceived cost of vaccination relative to the cost of infection. This allowed us not to rely on other uncertain epidemiological model parameters and, in particular, to bypass uncertainties about the role of the carriers in the transmission.

A game-theoretic model of Monkeypox to assess vaccination strategies

Monkeypox (MPX) is a zoonotic disease similar to smallpox. Its fatality rate is about 11% and it is endemic to the Central and West African countries. In this paper, we analyze a compartmental model of MPX dynamics. Our goal is to see whether MPX can be controlled and eradicated by voluntary vaccinations. We show that there are three equilibria—disease free, fully endemic and previously neglected semi-endemic (with disease existing only among humans). The existence of semi-endemic equilibrium has severe implications should the MPX virus mutate to increased viral fitness in humans. We find that MPX is controllable and can be eradicated in a semi-endemic equilibrium by vaccination. However, in a fully endemic equilibrium, MPX cannot be eradicated by vaccination alone.

Game-Theoretical Model of Retroactive Hepatitis B Vaccination in China

Hepatitis B (HepB) is one of the most common infectious diseases affecting over two billion people worldwide. About one third of all HepB cases are in China. In recent years, China made significant efforts to implement a nationwide HepB vaccination program and reduced the number of unvaccinated infants from 30 to 10%. However, many individuals still remain unprotected, particularly those born before 2003. Consequently, a catch-up retroactive vaccination is an important and potentially cost-effective way to reduce HepB prevalence. In this paper, we analyze a game theoretical model of HepB dynamics that incorporates government-provided vaccination at birth coupled with voluntary retroactive vaccinations. Given the uncertainty about the long-term efficacy of the HepB vaccinations, we study several scenarios. When the waning rate is relatively high, we show that this retroactive vaccination should be a necessary component of any HepB eradication effort. When the vaccine offers long-lasting protection, the voluntary retroactive vaccination brings the disease incidence to sufficiently low levels. Also, we find that the optimal vaccination rates are almost independent of the vaccination coverage at birth. Moreover, it is in an individual's self-interest to vaccinate (and potentially re-vaccinate) at a rate just slightly above the vaccine waning rate.

A game-theoretical analysis of poliomyelitis vaccination

Poliomyelitis is a worldwide disease that has nearly been eradicated thanks to the Global Polio Eradication Initiative. Nevertheless, the disease is currently still endemic in three countries. In this paper, we incorporate the vaccination in a two age-class model of polio dynamics. Our main objective is to see whether mandatory vaccination policy is needed or if polio could be almost eradicated by a voluntary vaccination. We perform game theoretical analysis and compare the herd immunity vaccination levels with the Nash equilibrium vaccination levels. We show that the gap between two vaccination levels is too large. We conclude that the mandatory vaccination policy is therefore needed to achieve a complete eradication.

Willingness-to-pay for a hypothetical Ebola vaccine in Indonesia: A cross-sectional study in Aceh

Background: Some Ebola vaccines have been developed and tested in phase III clinical trials. However, assessment of whether public have willingness to purchase or not, especially in unaffected areas, is lacking. The aim of this study was to determine willingness to pay (WTP) for a hypothetical Ebola vaccine in Indonesia.

Methods: A cross-sectional study was conducted from 1 August to 30 December 2015 in five cities in Aceh province of Indonesia. Patients’ family members who visited outpatient departments were approached and interviewed about their sociodemographic characteristics, knowledge of Ebola, attitude towards vaccination practice and their WTP for a hypothetical Ebola vaccine. A multivariable linear regression model assessed the relationship between these explanatory variables and WTP.

Results: During the study, 500 participants were approached and interviewed. There were 424 (84.8%) respondents who completed the interview and 74% (311/424) expressed their acceptance for an Ebola vaccine. There were 288 participants who were willing to pay for an Ebola vaccine (92.6% out of 311). The mean of WTP was US$2.08 (95% CI: 1.75-2.42). The final multivariable model indicated that young age, high educational attainment, working as a private employee, entrepreneur or civil servant (compared to farmers), being unmarried, and residing in a suburb (compared to a city) were associated with higher WTP.

Conclusions: Although the proportion of the participants who would accept the Ebola vaccine was relatively high, the amount they were willing to pay for Ebola vaccine was very low. This finding would indicate the need of subsidies for Ebola vaccine in the country.

Willingness-to-pay for a hypothetical Ebola vaccine in Indonesia: A cross-sectional study in Aceh

Background: Some Ebola vaccines have been developed and tested in phase III clinical trials. However, assessment of whether public have willingness to purchase or not, especially in unaffected areas, is lacking. The aim of this study was to determine willingness to pay (WTP) for a hypothetical Ebola vaccine in Indonesia. Methods: A cross-sectional study was conducted from 1 August to 30 December 2015 in five cities in Aceh province of Indonesia. Patients' family members who visited outpatient departments were approached and interviewed about their sociodemographic characteristics, knowledge of Ebola, attitude towards vaccination practice and their WTP for a hypothetical Ebola vaccine. A multivariable linear regression model assessed the relationship between these explanatory variables and WTP. Results: During the study, 500 participants were approached and interviewed. There were 424 (84.8%) respondents who completed the interview and 74% (311/424) expressed their acceptance for an Ebola vaccine. There were 288 participants who were willing to pay for an Ebola vaccine (92.6% out of 311). The mean of WTP was US$2.08 (95% CI: 1.75-2.42). The final multivariable model indicated that young age, high educational attainment, working as a private employee, entrepreneur or civil servant (compared to farmers), being unmarried, and residing in a suburb (compared to a city) were associated with higher WTP. Conclusions: Although the proportion of the participants who would accept the Ebola vaccine was relatively high, the amount they were willing to pay for Ebola vaccine was very low. This finding would indicate the need of subsidies for Ebola vaccine in the country.

Willingness-to-pay for a hypothetical Ebola vaccine in Indonesia: A cross-sectional study in Aceh

Background: Some Ebola vaccines have been developed and tested in phase III clinical trials. However, assessment of whether public have willingness to purchase or not, especially in unaffected areas, is lacking. The aim of this study was to determine willingness to pay (WTP) for a hypothetical Ebola vaccine in Indonesia. Methods: A cross-sectional study was conducted from 1 August to 30 December 2015 in five cities in Aceh province of Indonesia. Patients' family members who visited outpatient departments were approached and interviewed about their sociodemographic characteristics, knowledge of Ebola, attitude towards vaccination practice and their WTP for a hypothetical Ebola vaccine. A multivariable linear regression model assessed the relationship between these explanatory variables and WTP. Results: During the study, 500 participants were approached and interviewed. There were 424 (84.8%) respondents who completed the interview and 74% (311/424) expressed their acceptance for an Ebola vaccine. There were 288 participants who were willing to pay for an Ebola vaccine (92.6% out of 311). The mean of WTP was US$2.08 (95% CI: 1.75-2.42). The final multivariable model indicated that young age, high educational attainment, working as a private employee, entrepreneur or civil servant (compared to farmers), being unmarried, and residing in a suburb (compared to a city) were associated with higher WTP. Conclusions: Although the proportion of the participants who would accept the Ebola vaccine was relatively high, the amount they were willing to pay for Ebola vaccine was very low. This finding would indicate the need of subsidies for Ebola vaccine in the country.

Intranasal vaccination with ebola virus GP amino acids 258-601 protects mice against lethal challenge

Ebola virus (EBOV) disease (EVD) leads to lethal hemorrhagic fever with a case fatality rate as high as 90%, thus posing a serious global public health concern. However, while several vaccines based on the EBOV glycoprotein have been confirmed to be effective in animal experiments, no licensed vaccines or effective treatments have been approved since the first outbreak was reported in 1976. In this study, we prepared the extracellular domain of the EBOV GP protein (designated as N20) by prokaryotic expression and purification via chromatography. Using CTA1-DD (designated as H45) as a mucosal adjuvant, we evaluated the immunogenicity of N20 by intranasal administration and the associated protective efficacy against mouse-adapted EBOV challenge in mice. We found that intranasal vaccination with H45-adjuvanted N20 could stimulate humoral immunity, as supported by GP-specific IgG titers; Th1 cellular immunity, based on IgG subclasses and IFN-γ/IL-4 secreting cells; and mucosal immunity, based on the presence of anti-EBOV IgA in vaginal lavages. We also confirmed that the vaccine could completely protect mice against a lethal mouse-adapted EBOV (MA-EBOV) challenge with few side effects (based on weight loss). In comparison, mice that received N20 or H45 alone succumbed to lethal MA-EBOV challenge. Therefore, mucosal vaccination with H45-adjuvanted N20 represents a potential vaccine candidate for the prevention of EBOV in an effective, safe, and convenient manner.