Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries.

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.

Unraveling the dynamics of the Omicron and Delta variants of the 2019 coronavirus in the presence of vaccination, mask usage, and antiviral treatment.

The effectiveness of control interventions against COVID-19 is threatened by the emergence of SARS-CoV-2 variants of concern. We present a mathematical model for studying the transmission dynamics of two of these variants (Delta and Omicron) in the United States, in the presence of vaccination, treatment of individuals with clinical symptoms of the disease and the use of face masks. The model is parameterized and cross-validated using observed daily case data for COVID-19 in the United States for the period from November 2021 (when Omicron first emerged) to March 2022. Rigorous qualitative analysis of the model shows that the disease-free equilibrium of the model is locally-asymptotically stable when the control reproduction number of the model (denoted by R c ) is less than one. This equilibrium is shown to be globally-asymptotically stable for a special case of the model, where disease-induced mortality is negligible and both vaccine-derived immunity in fully-vaccinated individuals and natural immunity do not wane, when the associated reproduction number is less than one. The epidemiological implication of the latter result is that the combined vaccination-boosting strategy can lead to the elimination of the pandemic if its implementation can bring (and maintain) the associated reproduction number to a value less than one. An analytical expression for the vaccine-derived herd immunity threshold is derived. Using this expression, together with the baseline values of the parameters of the parameterized model, we showed that the vaccine-derived herd immunity can be achieved in the United States (so that the pandemic will be eliminated) if at least 68 % of the population is fully-vaccinated with two of the three vaccines approved for use in the United States (Pfizer or Moderna vaccine). Furthermore, this study showed (as of the time of writing in March 2022) that the control reproduction number of the Omicron variant was approximately 3.5 times that of the Delta variant (the reproduction of the latter is computed to be ≈ 0.2782 ), indicating that Delta had practically died out and that Omicron has competitively-excluded Delta (to become the predominant variant in the United States). Based on our analysis and parameterization at the time of writing of this paper (March 2022), our study suggests that SARS-CoV-2 elimination is feasible by June 2022 if the current baseline level of the coverage of fully-vaccinated individuals is increased by about 20 % . The prospect of pandemic elimination is significantly improved if vaccination is combined with a face mask strategy that prioritizes moderately effective and high-quality masks. Having a high percentage of the populace wearing the moderately-effective surgical mask is more beneficial to the community than having low percentage of the populace wearing the highly-effective N95 masks. We showed that waning natural and vaccine-derived immunity (if considered individually) offer marginal impact on disease burden, except for the case when they wane at a much faster rate (e.g., within three months), in comparison to the baseline (estimated to be within 9 months to a year). Treatment of symptomatic individuals has marginal effect in reducing daily cases of SARS-CoV-2, in comparison to the baseline, but it has significant impact in reducing daily hospitalizations. Furthermore, while treatment significantly reduces daily hospitalizations (and, consequently, deaths), the prospects of COVID-19 elimination in the United States are significantly enhanced if investments in control resources are focused on mask usage and vaccination rather than on treatment.

Assessing the impact of insecticide-treated nets in the face of insecticide resistance on malaria control.

The mosquito-borne disease, malaria, continues to impose a devastating health and economic burden worldwide. In malaria-endemic areas, insecticide-treated nets (ITNs) have been useful in curtailing the burden of the disease. However, mosquito resistance to insecticides, decay in ITN efficacy, net attrition, etc., undermine the effectiveness of ITNs in combatting malaria. In this study, mathematical models that account for asymptomatic infectious humans (through a partially immune class or a separate asymptomatic infectious class), insecticide resistance, and decay in ITN efficacy are proposed and analyzed. Analytical and numerical results of the models when ITN efficacy is constant show that there are parameter regimes for which a backward bifurcation occurs. Local and global sensitivity analyses are performed to identify parameters (some of which are potential targets for disease control) with the most significant influence on the control reproduction (Rc) and disease prevalence. These influential parameters include the maximum biting rate of resistant mosquitoes, ITN coverage, initial ITN efficacy against sensitive mosquitoes, the probability that an infectious mosquito (human) infects a susceptible human (mosquito), and the rate at which adult mosquitoes develop (lose) resistance to insecticides. Simulations of the models show that accounting for asymptomatic infectious humans through a separate class, or not accounting for the decay in ITN efficacy leads to an underestimation of disease burden. In particular, if the initial efficacy of ITNs against sensitive and resistance mosquitoes is 96%, the minimum ITN coverage required to reduce Rc below one (and hence, contain malaria) is approximately 11% (27%) lower when ITN efficacy is averaged (constant) for a model with a separate asymptomatic class. For the model with a partially immune class and decaying ITN efficacy, reducing Rc below one is impossible even if the entire populace uses ITNs. The study shows that replacing ITNs before their prescribed lifespans, or designing ITNs with longer lifespans is important for malaria control. Furthermore, the study shows that piperonyl butoxide (PBO) ITNs (which inhibit or reverse insecticide resistance) outperform regular ITNs in malaria control. Hence, prospects for effectively controlling malaria are enhanced by widespread use of high quality ITNs (e.g. PBO ITNs), especially if the useful lifespans of the ITNs are long enough and the ITNs are replaced before the end of their useful lifespans.

Warming temperatures could expose more than 1.3 billion new people to Zika virus risk by 2050.

In the aftermath of the 2015 pandemic of Zika virus (ZIKV), concerns over links between climate change and emerging arboviruses have become more pressing. Given the potential that much of the world might remain at risk from the virus, we used a previously established temperature-dependent transmission model for ZIKV to project climate change impacts on transmission suitability risk by mid-century (a generation into the future). Based on these model predictions, in the worst-case scenario, over 1.3 billion new people could face suitable transmission temperatures for ZIKV by 2050. The next generation will face substantially increased ZIKV transmission temperature suitability in North America and Europe, where naïve populations might be particularly vulnerable. Mitigating climate change even to moderate emissions scenarios could significantly reduce global expansion of climates suitable for ZIKV transmission, potentially protecting around 200 million people. Given these suitability risk projections, we suggest an increased priority on research establishing the immune history of vulnerable populations, modeling when and where the next ZIKV outbreak might occur, evaluating the efficacy of conventional and novel intervention measures, and increasing surveillance efforts to prevent further expansion of ZIKV.

Human choice to self-isolate in the face of the COVID-19 pandemic: A game dynamic modelling approach.

Non-pharmaceutical interventions (NPIs) involving social-isolation strategies such as self-quarantine (SQ) and social-distancing (SD) are useful in controlling the spread of infections that are transmitted through human-to-human contacts, e.g., respiratory diseases such as COVID-19. In the absence of a safe and effective cure or vaccine during the first ten months of the COVID-19 pandemic, countries around the world implemented these social-isolation strategies and other NPIs to reduce COVID-19 transmission. But, individual and public perception play a crucial role in the success of any social-isolation measure. Thus, in spite of governments' initiatives to use NPIs to combat COVID-19 in many countries around the world, individual choices rendered social-isolation unsuccessful in some of these countries. This resulted in huge outbreaks that imposed a substantial morbidity, mortality, hospitalization, economic, etc., toll on human lives. In particular, human choices pose serious challenges to public health strategic decision-making in controlling the COVID-19 pandemic. To unravel the impact of this behavioral response to social-isolation on the burden of the COVID-19 pandemic, we develop a model framework that integrates COVID-19 transmission dynamics with a multi-strategy evolutionary game approach of individual decision-making. We use this integrated framework to characterize the evolution of human choices in social-isolation as the disease progresses and public health control measures such as mandatory lockdowns are implemented. Analysis of the model illustrates that SD plays a major role in reducing the burden of the disease compared to SQ. Parameter estimation using COVID-19 incidence data, as well as different lockdown data sets from India, and scenario analysis involving a combination of Voluntary-Mandatory implementation of SQ and SD shows that the effectiveness of this approach depends on the type of isolation, and the time and period of implementation of the selected isolation measure during the outbreak.

Temperature drives Zika virus transmission: evidence from empirical and mathematical models.

Temperature is a strong driver of vector-borne disease transmission. Yet, for emerging arboviruses we lack fundamental knowledge on the relationship between transmission and temperature. Current models rely on the untested assumption that Zika virus responds similarly to dengue virus, potentially limiting our ability to accurately predict the spread of Zika. We conducted experiments to estimate the thermal performance of Zika virus (ZIKV) in field-derived Aedes aegypti across eight constant temperatures. We observed strong, unimodal effects of temperature on vector competence, extrinsic incubation period and mosquito survival. We used thermal responses of these traits to update an existing temperature-dependent model to infer temperature effects on ZIKV transmission. ZIKV transmission was optimized at 29°C, and had a thermal range of 22.7°C-34.7°C. Thus, as temperatures move towards the predicted thermal optimum (29°C) owing to climate change, urbanization or seasonality, Zika could expand north and into longer seasons. By contrast, areas that are near the thermal optimum were predicted to experience a decrease in overall environmental suitability. We also demonstrate that the predicted thermal minimum for Zika transmission is 5°C warmer than that of dengue, and current global estimates on the environmental suitability for Zika are greatly over-predicting its possible range.

Poverty, disease, and the ecology of complex systems.

Understanding why some human populations remain persistently poor remains a significant challenge for both the social and natural sciences. The extremely poor are generally reliant on their immediate natural resource base for subsistence and suffer high rates of mortality due to parasitic and infectious diseases. Economists have developed a range of models to explain persistent poverty, often characterized as poverty traps, but these rarely account for complex biophysical processes. In this Essay, we argue that by coupling insights from ecology and economics, we can begin to model and understand the complex dynamics that underlie the generation and maintenance of poverty traps, which can then be used to inform analyses and possible intervention policies. To illustrate the utility of this approach, we present a simple coupled model of infectious diseases and economic growth, where poverty traps emerge from nonlinear relationships determined by the number of pathogens in the system. These nonlinearities are comparable to those often incorporated into poverty trap models in the economics literature, but, importantly, here the mechanism is anchored in core ecological principles. Coupled models of this sort could be usefully developed in many economically important biophysical systems--such as agriculture, fisheries, nutrition, and land use change--to serve as foundations for deeper explorations of how fundamental ecological processes influence structural poverty and economic development.

Interplay between insecticide-treated bed-nets and mosquito demography: implications for malaria control.

Although malaria prevalence has witnessed a significant reduction within the past decade, malaria still constitutes a major health and economic problem, especially to low-income countries. Insecticide-treated nets (ITNs) remain one of the primary measures for preventing the malignant disease. Unfortunately, the success of ITN campaigns is hampered by improper use and natural decay in ITN-efficacy over time. Many models aimed at studying malaria transmission and control fail to account for this decay, as well as mosquito demography and feeding preferences exhibited by mosquitoes towards humans. Omitting these factors can misrepresent disease risk, while understanding their effects on malaria dynamics can inform control policy. We present a model for malaria dynamics that incorporates these factors, and a systematic analysis, including stability and sensitivity analyses of the model under different conditions. The model with constant ITN-efficacy exhibits a backward bifurcation emphasizing the need for sustained control measures until the basic reproduction number, R0, drops below a critical value at which control is feasible. The infectious and partially immune human populations and R0 are highly sensitive to the probability that a mosquito feeds successfully on a human, ITN coverage and the maximum biting rate of mosquitoes, irrespective of whether ITN-efficacy is constant or declines over time. This implies that ITNs play an important role in disease control. When ITN-efficacy wanes over time, we identify disease risks and corresponding ITN coverage, as well as feeding preference levels for which the disease can be controlled or eradicated. Our study leads to important insights that could assist in the design and implementation of better malaria control strategies. We conclude that ITNs that can retain their effectiveness for longer periods will be more appropriate in the fight against malaria and that making more ITNs available to highly endemic regions is necessary for malaria containment.

Economic inequality caused by feedbacks between poverty and the dynamics of a rare tropical disease: the case of Buruli ulcer in sub-Saharan Africa.

Neglected tropical diseases (NTDs) have received increasing attention in recent years by the global heath community, as they cumulatively constitute substantial burdens of disease as well as barriers for economic development. A number of common tropical diseases such as malaria, hookworm or schistosomiasis have well-documented economic impacts. However, much less is known about the population-level impacts of diseases that are rare but associated with high disability burden, which represent a great number of tropical diseases. Using an individual-based model of Buruli ulcer (BU), we demonstrate that, through feedbacks between health and economic status, such NTDs can have a significant impact on the economic structure of human populations even at low incidence levels. While average wealth is only marginally affected by BU, the economic conditions of certain subpopulations are impacted sufficiently to create changes in measurable population-level inequality. A reduction of the disability burden caused by BU can thus maximize the economic growth of the poorest subpopulations and reduce significantly the economic inequalities introduced by the disease in endemic regions.

Persistent oscillations and backward bifurcation in a malaria model with varying human and mosquito populations: implications for control.

We derive and study a deterministic compartmental model for malaria transmission with varying human and mosquito populations. Our model considers disease-related deaths, asymptomatic immune humans who are also infectious, as well as mosquito demography, reproduction and feeding habits. Analysis of the model reveals the existence of a backward bifurcation and persistent limit cycles whose period and size is determined by two threshold parameters: the vectorial basic reproduction number Rm, and the disease basic reproduction number R0, whose size can be reduced by reducing Rm. We conclude that malaria dynamics are indeed oscillatory when the methodology of explicitly incorporating the mosquito's demography, feeding and reproductive patterns is considered in modeling the mosquito population dynamics. A sensitivity analysis reveals important control parameters that can affect the magnitudes of Rm and R0, threshold quantities to be taken into consideration when designing control strategies. Both Rm and the intrinsic period of oscillation are shown to be highly sensitive to the mosquito's birth constant λm and the mosquito's feeding success probability pw. Control of λm can be achieved by spraying, eliminating breeding sites or moving them away from human habitats, while pw can be controlled via the use of mosquito repellant and insecticide-treated bed-nets. The disease threshold parameter R0 is shown to be highly sensitive to pw, and the intrinsic period of oscillation is also sensitive to the rate at which reproducing mosquitoes return to breeding sites. A global sensitivity and uncertainty analysis reveals that the ability of the mosquito to reproduce and uncertainties in the estimations of the rates at which exposed humans become infectious and infectious humans recover from malaria are critical in generating uncertainties in the disease classes.

Quantifying the impact of decay in bed-net efficacy on malaria transmission.

Insecticide-treated nets (ITNs) are at the forefront of malaria control programs and even though the percentage of households in sub-Saharan Africa that owned nets increased from 3% in 2000 to 53% in 2012, many children continue to die from malaria. The potential impact of ITNs on reducing malaria transmission is limited due to inconsistent or improper use, as well as physical decay in effectiveness. Most mathematical models for malaria transmission have assumed a fixed effectiveness rate for bed-nets, which can overestimate the impact of nets on malaria control. We develop a model for malaria spread that captures the decrease in ITN effectiveness due to physical and chemical decay, as well as human behavior as a function of time. We perform uncertainty and sensitivity analyses to identify and rank parameters that play a critical role in malaria transmission. These analyses show that the basic reproduction number R0, and the infectious human population are most sensitive to bed-net coverage and the biting rate of mosquitoes. Our results show the existence of a backward bifurcation for the case in which ITN efficacy is constant over time, which occurs for some range of parameters and is characterized by high malaria mortality in humans. This result implies that bringing R0 to less than one is not enough for malaria elimination but rather additional efforts will be necessary to control the disease. For the case in which ITN efficacy decays over time, we determine coverage levels required to control malaria for different ITN efficacies and demonstrate that ITNs with longer useful lifespans perform better in malaria control. We conclude that malaria control programs should focus on increasing bed-net coverage, which can be achieved by enhancing malaria education and increasing bed-net distribution in malaria endemic regions.

Modeling the synergistic interplay between malaria dynamics and economic growth.

The mosquito-borne disease (malaria) imposes significant challenges on human health, healthcare systems, and economic growth/productivity in many countries. This study develops and analyzes a model to understand the interplay between malaria dynamics, economic growth, and transient events. It uncovers varied effects of malaria and economic parameters on model outcomes, highlighting the interdependence of the reproduction number (R0) on both malaria and economic factors, and a reciprocal relationship where malaria diminishes economic productivity, while higher economic output is associated with reduced malaria prevalence. This emphasizes the intricate interplay between malaria dynamics and socio-economic factors. The study offers insights into malaria control and underscores the significance of optimizing external aid allocation, especially favoring an even distribution strategy, with the most significant reduction observed in an equal monthly distribution strategy compared to longer distribution intervals. Furthermore, the study shows that controlling malaria in high mosquito biting areas with limited aid, low technology, inadequate treatment, or low economic investment is challenging. The model exhibits a backward bifurcation implying that sustainability of control and mitigation measures is essential even when R0 is slightly less than one. Additionally, there is a parameter regime for which long transients are feasible. Long transients are critical for predicting the behavior of dynamic systems and identifying factors influencing transitions; they reveal reservoirs of infection, vital for disease control. Policy recommendations for effective malaria control from the study include prioritizing sustained control measures, optimizing external aid allocation, and reducing mosquito biting.

The impact of bed-net use on malaria prevalence.

Malaria infection continues to be a major problem in many parts of the world including the Americas, Asia, and Africa. Insecticide-treated bed-nets have shown to reduce malaria cases by 50%; however, improper handling and human behavior can diminish their effectiveness. We formulate and analyze a mathematical model that considers the transmission dynamics of malaria infection in mosquito and human populations and investigate the impact of bed-nets on its control. The effective reproduction number is derived and existence of backward bifurcation is presented. The backward bifurcation implies that the reduction of R below unity alone is not enough to eradicate malaria, except when the initial cases of infection in both populations are small. Our analysis demonstrate that bed-net usage has a positive impact in reducing the reproduction number R. The results show that if 75% of the population were to use bed-nets, malaria could be eliminated. We conclude that more data on the impact of human and mosquito behavior on malaria spread is needed to develop more realistic models and better predictions.

The impact of temperature and decay in insecticide-treated net efficacy on malaria prevalence and control.

Insecticide-treated nets (ITNs) have been useful and effective in mitigating the risk of malaria globally. However, due to misuse and normal/human-induced physical and chemical wear, the effectiveness of ITNs in combating malaria has been declining. Underlying heterogeneities in the nature of malaria, combined with environmental factors such as temperature lead to complex malaria transmission and control dynamics. In particular, temperature plays a significant role in determining the risk of malaria since it influences the growth and survival of mosquitoes and the malaria parasite. Here, a unifying mechanistic framework that integrates malaria dynamics with waning ITN-efficacy and temperature change is developed and used to assess the impact of interactions between significant sources of variation (e.g., temperature) and waning ITN-efficacy on the risk of malaria transmission and the success of ITN programs. The model exhibits a backward bifurcation when ITN-efficacy is constant implying that control efforts must be stepped up and sustained a bit longer even when the reproduction number is slightly less than one. The study shows that malaria is more effectively controlled with ITNs that have a longer lifespan and if ITNs are replaced before the end of their expiration period. Also, failing to account for waning ITN-efficacy leads to an underestimation of disease risk, burden, and effort level required to contain the disease. Local and global sensitivity analyses show that control and temperature-related parameters are primary drivers of the reproduction number and the human disease burden, highlighting the significance of temperature on malaria dynamics. Furthermore, the study shows that the human disease burden is optimal at a temperature of ≈28°C and that high seasonal variations can trigger major malaria outbreaks even in regions with low mean temperatures. Additionally, accounting for both seasonality and decay in ITN-efficacy leads to complex malaria patterns. To sum it up, insights into the sensitivity of malaria dynamics on temperature are useful in assessing the potential impact of changes in temperature on malaria risk. Also, a malaria control program, which ensures that ITNs are replaced regularly and early enough, and that educates at risk populations on proper use and care for ITNs is necessary for reducing the burden of malaria.

Mathematical assessment of the role of waning and boosting immunity against the BA.1 Omicron variant in the United States.

Three safe and effective vaccines against SARS-CoV-2 have played a major role in combating COVID-19 in the United States. However, the effectiveness of these vaccines and vaccination programs has been challenged by the emergence of new SARS-CoV-2 variants of concern. A new mathematical model is formulated to assess the impact of waning and boosting of immunity against the Omicron variant in the United States. To account for gradual waning of vaccine-derived immunity, we considered three vaccination classes that represent high, moderate and low levels of immunity. We showed that the disease-free equilibrium of the model is globally-asymptotically, for two special cases, if the associated reproduction number is less than unity. Simulations of the model showed that vaccine-derived herd immunity can be achieved in the United States via a vaccination-boosting strategy which entails fully vaccinating at least 59% of the susceptible populace followed by the boosting of about 72% of the fully-vaccinated individuals whose vaccine-derived immunity has waned to moderate or low level. In the absence of boosting, waning of immunity only causes a marginal increase in the average number of new cases at the peak of the pandemic, while boosting at baseline could result in a dramatic reduction in the average number of new daily cases at the peak. Specifically, for the fast immunity waning scenario (where both vaccine-derived and natural immunity are assumed to wane within three months), boosting vaccine-derived immunity at baseline reduces the average number of daily cases at the peak by about 90% (in comparison to the corresponding scenario without boosting of the vaccine-derived immunity), whereas boosting of natural immunity (at baseline) only reduced the corresponding peak daily cases (in comparison to the corresponding scenario without boosting of natural immunity) by approximately 62%. Furthermore, boosting of vaccine-derived immunity is more beneficial (in reducing the burden of the pandemic) than boosting of natural immunity. Finally, boosting vaccine-derived immunity increased the prospects of altering the trajectory of COVID-19 from persistence to possible elimination.

Mathematical model on HIV and nutrition.

HIV continues to be a major global health issue, having claimed millions of lives in the last few decades. While several empirical studies support the fact that proper nutrition is useful in the fight against HIV, very few studies have focused on developing and using mathematical modelling approaches to assess the association between HIV, human immune response to the disease, and nutrition. We develop a within-host model for HIV that captures the dynamic interactions between HIV, the immune system and nutrition. We find that increased viral activity leads to increased serum protein levels. We also show that the viral production rate is positively correlated with HIV viral loads, as is the enhancement rate of protein by virus. Although our numerical simulations indicate a direct correlation between dietary protein intake and serum protein levels in HIV-infected individuals, further modelling and clinical studies are necessary to gain comprehensive understanding of the relationship.

Critical assessment of the impact of vaccine-type and immunity on the burden of COVID-19.

The COVID-19 pandemic continues to have a devastating impact on health systems and economies across the globe. Implementing public health measures in tandem with effective vaccination strategies have been instrumental in curtailing the burden of the pandemic. With the three vaccines authorized for use in the U.S. having varying efficacies and waning effects against major COVID-19 strains, understanding the impact of these vaccines on COVID-19 incidence and fatalities is critical. Here, we formulate and use mathematical models to assess the impact of vaccine type, vaccination and booster uptake, and waning of natural and vaccine-induced immunity on the incidence and fatalities of COVID-19 and to predict future trends of the disease in the U.S. when existing control measures are reinforced or relaxed. The results show a 5-fold reduction in the control reproduction number during the initial vaccination period and a 1.8-fold (2-fold) reduction in the control reproduction number during the initial first booster (second booster) uptake period, compared to the respective previous periods. Due to waning of vaccine-induced immunity, vaccinating up to 96% of the U.S. population might be required to attain herd immunity, if booster uptake is low. Additionally, vaccinating and boosting more people from the onset of vaccination and booster uptake, especially with the Pfizer-BioNTech and Moderna vaccines (which confer superior protection than the Johnson & Johnson vaccine) would have led to a significant reduction in COVID-19 cases and deaths in the U.S. Furthermore, adopting natural immunity-boosting measures is important in fighting COVID-19 and transmission rate reduction measures such as mask-use are critical in combating COVID-19. The emergence of a more transmissible COVID-19 variant, or early relaxation of existing control measures can lead to a more devastating wave, especially if transmission rate reduction measures and vaccination are relaxed simultaneously, while chances of containing the pandemic are enhanced if both vaccination and transmission rate reduction measures are reinforced simultaneously. We conclude that maintaining or improving existing control measures, and boosting with mRNA vaccines are critical in curtailing the burden of the pandemic in the U.S.

An evolutionary game model of individual choices and bed net use: elucidating key aspect in malaria elimination strategies.

Insecticide-treated net (ITN) is the most applicable and cost-effective malaria intervention measure in sub-Saharan Africa and elsewhere. Although ITNs have been widely distributed to malaria-endemic regions in the past, their success has been threatened by misuses (in fishing, agriculture etc.) and decay in ITN efficacy. Decision-making in using the ITNs depends on multiple coevolving factors: malaria prevalence, mosquito density, ITN availability and its efficacy, and other socio-economic determinants. While ITN misuse increases as the efficacy of ITNs declines, high efficacy also impedes proper use due to free-riding. This irrational usage leads to increased malaria prevalence, thereby worsening malaria control efforts. It also remains unclear if the optimum ITN use for malaria elimination can be achieved under such an adaptive social learning process. Here, we incorporate evolutionary game theory into a disease transmission model to demonstrate these behavioural interactions and their impact on malaria prevalence. We show that social optimum usage is a function of transmission potential, ITN efficacy and mosquito demography. Under specific parameter regimes, our model exhibits patterns of ITN usage similar to observed data from parts of Africa. Our study suggests that the provision of financial incentives as prompt feedback to improper ITN use can reduce misuse and contribute positively towards malaria elimination efforts in Africa and elsewhere.

The impact of age structure and vaccine prioritization on COVID-19 in West Africa.

The ongoing COVID-19 pandemic has been a major global health challenge since its emergence in 2019. Contrary to early predictions that sub-Saharan Africa (SSA) would bear a disproportionate share of the burden of COVID-19 due to the region's vulnerability to other infectious diseases, weak healthcare systems, and socioeconomic conditions, the pandemic's effects in SSA have been very mild in comparison to other regions. Interestingly, the number of cases, hospitalizations, and disease-induced deaths in SSA remain low, despite the loose implementation of non-pharmaceutical interventions (NPIs) and the low availability and administration of vaccines. Possible explanations for this low burden include epidemiological disparities, under-reporting (due to limited testing), climatic factors, population structure, and government policy initiatives. In this study, we formulate a model framework consisting of a basic model (in which only susceptible individuals are vaccinated), a vaccine-structured model, and a hybrid vaccine-age-structured model to assess the dynamics of COVID-19 in West Africa (WA). The framework is trained with a portion of the confirmed daily COVID-19 case data for 16 West African countries, validated with the remaining portion of the data, and used to (i) assess the effect of age structure on the incidence of COVID-19 in WA, (ii) evaluate the impact of vaccination and vaccine prioritization based on age brackets on the burden of COVID-19 in the sub-region, and (iii) explore plausible reasons for the low burden of COVID-19 in WA compared to other parts of the world. Calibration of the model parameters and global sensitivity analysis show that asymptomatic youths are the primary drivers of the pandemic in WA. Also, the basic and control reproduction numbers of the hybrid vaccine-age-structured model are smaller than those of the other two models indicating that the disease burden is overestimated in the models which do not account for age-structure. This result is confirmed through the vaccine-derived herd immunity thresholds. In particular, a comprehensive analysis of the basic (vaccine-structured) model reveals that if 84%(73%) of the West African populace is fully immunized with the vaccines authorized for use in WA, vaccine-derived herd immunity can be achieved. This herd immunity threshold is lower (68%) for the hybrid model. Also, all three thresholds are lower (60% for the basic model, 51% for the vaccine-structured model, and 48% for the hybrid model) if vaccines of higher efficacies (e.g., the Pfizer or Moderna vaccine) are prioritized, and higher if vaccines of lower efficacy are prioritized. Simulations of the models show that controlling the COVID-19 pandemic in WA (by reducing transmission) requires a proactive approach, including prioritizing vaccination of more youths or vaccination of more youths and elderly simultaneously. Moreover, complementing vaccination with a higher level of mask compliance will improve the prospects of containing the pandemic. Additionally, simulations of the model predict another COVID-19 wave (with a smaller peak size compared to the Omicron wave) by mid-July 2022. Furthermore, the emergence of a more transmissible variant or easing the existing measures that are effective in reducing transmission will result in more devastating COVID-19 waves in the future. To conclude, accounting for age-structure is important in understanding why the burden of COVID-19 has been low in WA and sustaining the current vaccination level, complemented with the WHO recommended NPIs is critical in curbing the spread of the disease in WA.

Effects of social-distancing on infectious disease dynamics: an evolutionary game theory and economic perspective.

We propose two models inspired by the COVID-19 pandemic: a coupled disease-human behaviour (or disease-game theoretic), and a coupled disease-human behaviour-economic model, both of which account for the impact of social-distancing on disease control and economic growth. The models exhibit rich dynamical behaviour including multistable equilibria, a backward bifurcation, and sustained bounded periodic oscillations. Analyses of the first model suggests that the disease can be eliminated if everybody practices full social-distancing, but the most likely outcome is some level of disease coupled with some level of social-distancing. The same outcome is observed with the second model when the economy is weaker than the social norms to follow health directives. However, if the economy is stronger, it can support some level of social-distancing that can lead to disease elimination.