Exploring optimal control strategies in seasonally varying flu-like epidemics

Epidemic control by social distancing and vaccination: Optimal strategies and remarks on the COVID-19 Italian response policy

After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first phase, while the second phase also benefits from the arrival of vaccines. We analyzed the problem by an ad-hoc numerical algorithm under a strong hypothesis implying a high degree of prioritization to the protection of health from the epidemic attack, which we termed the "low attack rate" hypothesis. The outputs of the model were also compared with the data from the Italian COVID-19 experience to provide a crude assessment of the goodness of the enacted interventions prior to the onset of the Omicron variant.

Seasonality as a driver of pH1N12009 influenza vaccination campaign impact

Although the most recent respiratory virus pandemic was triggered by a Coronavirus, sustained and elevated prevalence of highly pathogenic avian influenza viruses able to infect mammalian hosts highlight the continued threat of pandemics of influenza A virus (IAV) to global health. Retrospective analysis of pandemic outcomes, including comparative investigation of intervention efficacy in different regions, provide important contributions to the evidence base for future pandemic planning. The swine-origin IAV pandemic of 2009 exhibited regional variation in onset, infection dynamics and annual infection attack rates (IARs). For example, the UK experienced three severe peaks of infection over two influenza seasons, whilst Australia experienced a single severe wave. We adopt a seasonally forced 2-subtype model for the transmission of pH1N12009 and seasonal H3N2 to examine the role vaccination campaigns may play in explaining differences in pandemic trajectories in temperate regions. Our model differentiates between the nature of vaccine- and infection-acquired immunity. In particular, we assume that immunity triggered by infection elicits heterologous cross-protection against viral shedding in addition to long-lasting neutralising antibody, whereas vaccination induces imperfect reduction in susceptibility. We employ an Approximate Bayesian Computation (ABC) framework to calibrate the model using data for pH1N12009 seroprevalence, relative subtype dominance, and annual IARs for Australia and the UK. Heterologous cross-protection substantially suppressed the pandemic IAR over the posterior, with the strength of protection against onward transmission inversely correlated with the initial reproduction number. We show that IAV pandemic timing relative to the usual seasonal influenza cycle influenced the size of the initial waves of pH1N12009 in temperate regions and the impact of vaccination campaigns.

Identification of dynamical changes of rabies transmission under quarantine: Community-based measures towards rabies elimination

Quarantine has been long used as a public health response to emerging infectious diseases, particularly at the onset of an epidemic when the infected proportion of a population remains identifiable and logistically tractable. In theory, the same logic should apply to low-incidence infections; however, the application and impact of quarantine in low prevalence settings appears less common and lacks a formal analysis. Here, we present a quantitative framework using a series of progressively more biologically realistic models of canine rabies in domestic dogs and from dogs to humans, a suitable example system to characterize dynamical changes under varying levels of dog quarantine. We explicitly incorporate health-seeking behaviour data to inform the modelling of contact-tracing and exclusion of rabies suspect and probable dogs that can be identified through bite-histories of patients presenting at anti-rabies clinics. We find that a temporary quarantine of rabies suspect and probable dogs provides a powerful tool to curtail rabies transmission, especially in settings where optimal vaccination coverage is yet to be achieved, providing a critical stopgap to reduce the number of human and animal deaths due to rabid bites. We conclude that whilst comprehensive measures including sensitive surveillance and large-scale vaccination of dogs will be required to achieve disease elimination and sustained freedom given the persistent risk of rabies re-introductions, quarantine offers a low-cost community driven solution to intersectoral health burden.

Mitigating biological epidemic on heterogeneous social networks

Recent Covid-19 pandemic has demonstrated the need of efficient epidemic outbreak management. We study the optimal control problem of minimizing the fraction of infected population by applying vaccination and treatment control strategies, while at the same time minimizing the cost of implementing them. We model the epidemic using the degree based Susceptible–Infected–Recovered (SIR) compartmental model. We study the impact of varying network topologies on the optimal epidemic management strategies and present results for the Erdős–Rényi, scale free, and real world networks. For efficient computational modeling we form groups of groups of degree classes, and apply separate vaccination and treatment control signals to each group. This allows us to identify the degree classes that play a significant role in mitigating the epidemic for a given network topology. We compare the optimal control strategy with non optimal strategies (constant control and no control) and study the effect of various model parameters on the system. We identify which strategy (vaccination/treatment) plays a significant role in controlling the epidemic on different network topologies. We also study the effect of the cost of vaccination and treatment controls on the resource allocation. We find that the optimal strategy achieves significant improvements over the non optimal heuristics for all networks studied in this paper. Our results may be of interest to governments and healthcare authorities for devising effective vaccination and treatment campaigns during an epidemic outbreak.

A nonlinear optimal control method against the spreading of epidemics

To define a vaccination policy and antiviral treatment against the spreading of viral infections a nonlinear optimal (H-infinity) control approach is proposed. Actually, because of the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities, there is need to implement optimal control against the epidemics deployment. In this approach, the state-space model of the epidemics dynamics undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is developed for the approximately linearized model of the epidemics. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Furthermore, the global asymptotic stability properties of the control scheme are proven through Lyapunov stability analysis. This paper’s results confirm that optimal control of the infectious disease dynamics allows for eliminating its spreading while also keeping moderate the consumption of the related medication, that is vaccines and antiviral drugs.

Optimal control of pattern formations for an SIR reaction-diffusion epidemic model

Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic. The extent of epidemic is positively correlated to NSPA. To effectively reduce NSPA of patterns under the large transmission rates, taken removed (recovery or isolation) rate as a control parameter, we consider the mathematical formulation and numerical solution of an optimal control problem for the SIR reaction-diffusion model. Numerical experiments demonstrate the effectiveness of our method in terms of control effect, control precision and control cost.

Prevalence and Associated Risk Factor of COVID-19 and Impacts of Meteorological and Social Variables on Its Propagation in Punjab, Pakistan

The current study identifies the spatial distribution of COVID-19 cases and its association with meteorological and social variables in Punjab (densely populated province of Pakistan). To identify the COVID-19 propagation, the weekly growth, recovery, and deaths rate have also been calculated. The geographic information system (GIS) has used to determine COVID-19 impacts on gender (male/female), age groups, and causalities over an affected population (km^-2) for the period of 11th March to 12th August, 2020 in each district of province. Our results show that 43 peak days (where daily positive cases were above 900) have been observed in Punjab during 27th May to 8th July, 2020. The high population density districts, i.e., Lahore and Islamabad, have been affected (five persons per square kilometers) due to COVID-19, whereas the maximum death tolls (> 50 persons per millions) have also been observed in these urban districts. The meteorological variables (temperature, humidity, heat index, and ultraviolet index) show negative significant relationship to basic reproduction number (R0), whereas daily COVID-19 cases are positively correlated to aerosols concentration at 95% confidence level. The government intervention (stringency index) shows a positive impact to reduce the COVID-19 cases over the province. Keeping in view the COVID-19 behavior and climatology of the region, it has been identified that the COVID-19 cases may likely to increase during the dry period (high concentration of aerosols) i.e., October-December, 2020 and post-spring season (April to June), 2021 in urban areas of Pakistan. This study provides an overview on districts vulnerability that would help the policy makers, health agencies to plan their activities to reduce the COVID-19 impacts.

Impact of Heat Index and Ultraviolet Index on COVID-19 in Major Cities of Pakistan

INTRODUCTION

The world population is under the grip of global pandemic of COVID-19. The present study analyzed relationship between meteorological parameters and COVID-19 in three major cities of Pakistan, that is, Karachi, Lahore, and Peshawar.

METHODS

The impacts of heat index (HI) and ultraviolet index (UVI) over daily COVID-19 cases have examined to identify its transmission and propagation. The significance of basic reproductive number (R0), growth rate (Gr) and doubling time (Td) of COVID-19 with HI and UVI was determined.

RESULTS

Both indices show a significant positive correlation (at 5% significance level) to R0, Td, and Gr of COVID-19 patients. Our results showed that the minimum threshold temperature of 33 °C for HI (with a positive variation of 3 °C to 5 °C) put a significant impact on new cases.

CONCLUSION

HI and UVI impacted significantly to decline COVID-19 cases over the region.

The effects of regional climatic condition on the spread of COVID-19 at global scale

The pandemic outbreak of the novel coronavirus epidemic disease (COVID-19) is spreading like a diffusion-reaction in the world and almost 208 countries and territories are being affected around the globe. It became a sever health and socio-economic problem, while the world has no vaccine to combat this virus. This research aims to analyze the connection between the fast spread of COVID-19 and regional climate parameters over a global scale. In this research, we collected the data of COVID-19 cases from the time of 1st reported case to the 5th June 2020 in different affected countries and regional climatic parameters data from January 2020 to 5th June 2020. It was found that most of the countries located in the relatively lower temperature region show a rapid increase in the COVID-19 cases than the countries locating in the warmer climatic regions despite their better socio-economic conditions. A correlation between metrological parameters and COVID-19 cases was observed. Average daylight hours are correlated to total the COVID-19 cases with a coefficient of determination of 0.42, while average high-temperature shows a correlation of 0.59 and 0.42 with total COVID-19 cases and death cases respectively. The finding of the study will help international health organizations and local administrations to combat and well manage the spread of COVID-19.

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.