A general structured model of a hermaphrodite population.

Both empirical and theoretical studies, have dealt with the question how to best optimize reproductive fitness for hermaphrodites, using models such as game theory or complicated energetic costs and benefits of mating displays. However, hermaphrodites exhibit a broad spectrum of sexual behaviors like simultaneous, sequential or lifetime gonochorist that cannot be explained using a unique formalism. A possible explanation of this diversity relies on the way these species maximize their fitness: Does the individual hermaphrodite split its time between strategies maximizing its instantaneous reproductive fitness or its evolutionary fitness? Here, we compare these two points of view and extend a game theoretical formalism to a sex allocation model that underlies all sexual behaviors as a result of a dynamic game whose payoff depends on the costs and benefits of sexual reproduction. Using this formalism, we prove that a simultaneous hermaphrodites strategy is stable even for high values of sex changing costs. Moreover, we prove that the stability of a sequential hermaphrodite is linked to the average energy allocated to the pure female strategy.

Understanding hermaphrodite species through game theory.

We investigate the existence and stability of sexual strategies (sequential hermaphrodite, successive hermaphrodite or gonochore) at a proximate level. To accomplish this, we constructed and analyzed a general dynamical game model structured by size and sex. Our main objective is to study how costs of changing sex and of sexual competition should shape the sexual behavior of a hermaphrodite. We prove that, at the proximate level, size alone is insufficient to explain the tendency for a pair of prospective copulants to elect the male sexual role by virtue of the disparity in the energetic costs of eggs and sperm. In fact, we show that the stability of sequential vs. simultaneous hermaphrodite depends on sex change costs, while the stability of protandrous vs. protogynous strategies depends on competition cost.

Comparative reconstruction of SARS-CoV-2 transmission in three African countries using a mathematical model integrating immunity data.

Objectives: Africa has experienced fewer COVID-19 cases and deaths than other regions, with a contrasting epidemiological situation between countries, raising questions regarding the determinants of disease spread in Africa. Methods: We built a susceptible-exposed-infected-recovered model including COVID-19 mortality data where recovery class is structured by specific immunization and modeled by a partial differential equation considering the opposed effects of immunity decline and immunization. This model was applied to Tunisia, Senegal, and Madagascar. Results: Senegal and Tunisia experienced two epidemic phases. Initially, infections emerged in naive individuals and were limited by social distancing. Variants of concern (VOCs) were also introduced. The second phase was characterized by successive epidemic waves driven by new VOCs that escaped host immunity. Meanwhile, Madagascar demonstrated a different profile, characterized by longer intervals between epidemic waves, increasing the pool of susceptible individuals who had lost their protective immunity. The impact of vaccination on model parameters in Tunisia and Senegal was evaluated. Conclusions: Loss of immunity and vaccination-induced immunity have played crucial role in controlling the African pandemic. SARS-CoV-2 has become endemic now and will continue to circulate in African populations. However, previous infections provide significant protection against severe diseases, thus providing a basis for future vaccination strategies.

Optimal vaccination strategies for a heterogeneous population using multiple objectives: The case of L1- and L2-formulations.

The choice of the objective functional in optimization problems coming from biomedical and epidemiological applications plays a key role in optimal control outcomes. In this study, we investigate the role of the objective functional on the structure of the optimal control solution for an epidemic model for sexually transmitted infections that includes a core group with higher sexual activity levels than the rest of the population. An optimal control problem is formulated to find a targeted vaccination program able to control the spread of the infection with minimum vaccine deployment. Both L1- and L2-objectives are considered as an attempt to explore the trade-offs between control dynamics and the functional form characterizing optimality. The results show that the optimal vaccination policies for both the L1- and the L2-formulation share one important qualitative property, that is, immunization of the core group should be prioritized by policymakers to achieve a fast reduction of the epidemic. However, quantitative aspects of this result can be significantly affected depending on the choice of the control weights between formulations. Overall, the results suggest that with appropriate weight constants, the optimal control outcomes are reasonably robust with respect to the L1- or L2-formulation. This is particularly true when the monetary cost of the control policy is substantially lower than the cost associated with the disease burden. Under these conditions, even if the L1-formulation is more realistic from a modeling perspective, the L2-formulation can be used as an approximation and yield qualitatively comparable outcomes.

Hospital bed capacity across in Tunisia hospital during the first 4 waves of the COVID-19 pandemic: A descriptive analysis.

Background: In March 2020, the WHO declared COVID-19 as a pandemic, and Tunisia implemented a containment and targeted screening strategy. The country's public health policy has since focused on managing hospital beds. Methods: The study analyzed the bed occupancy rates in public hospitals in Tunisia during the pandemic. The evolution of daily cases and nonpharmaceutical interventions (NPI) actions undertaken by the Tunisian Government were also analyzed. The study used 3 indices to assess bed flexibility: Ramp duration until the peak, ramp growth until the peak, and ramp rate until the peak. The study also calculated the time shift at the start and peak of each wave to evaluate the government's response efficacy. Results: The study found that the evolution of the epidemic in Tunisia had 2 phases. The first phase saw the pandemic being controlled due to strong NPI actions, while the second phase saw a relaxation of measures and an increase in wave intensity. ICU bed availability followed the demand for beds, but ICU bed occupancy remained high, with a maximum of 97%. The government's response in terms of bed distribution and reallocation was slow. The study found that the most deadly wave by ICU occupied bed was the third wave due to a historical variant, while the fifth wave due to the delta variant was the most deadly in terms of cumulative death. Conclusions: The study concluded that decision-makers could use its findings to assess their response capabilities in the current pandemic and future ones. The study highlighted the importance of flexible and responsive healthcare systems in managing pandemics.

Optimal control model of tumor treatment in the context of cancer stem cell.

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

Spatio-temporal evolution of the COVID-19 across African countries.

The aim of this study is to make a comparative study on the reproduction number R 0 computed at the beginning of each wave for African countries and to understand the reasons for the disparities between them. The study covers the two first years of the COVID-19 pandemic and for 30 African countries. It links pandemic variables, reproduction number R 0, demographic variable, median age of the population, economic variables, GDP and CHE per capita, and climatic variables, mean temperature at the beginning of each waves. The results show that the diffusion of COVID-19 in Africa was heterogeneous even between geographical proximal countries. The difference of the basic reproduction number R 0 values is very large between countries and is significantly correlated with economic and climatic variables GDP and temperature and to a less extent with the mean age of the population.

Non-pharmaceutical interventions and COVID-19 vaccination strategies in Senegal: a modelling study.

BACKGROUND: When vaccines against the novel COVID-19 were available in Senegal, many questions were raised. How long should non-pharmaceutical interventions (NPIs) be maintained during vaccination roll-out? What are the best vaccination strategies? METHODS: In this study, we used an age-structured dynamic mathematical model. This model uses parameters based on SARS-CoV-2 virus, information on different types of NPIs, epidemiological and demographic data, some parameters relating to hospitalisations and vaccination in Senegal. RESULTS: In all scenarios explored, the model predicts a larger third epidemic wave of COVID-19 in terms of new cases and deaths than the previous waves. In a context of limited vaccine supply, vaccination alone will not be sufficient to control the epidemic, and the continuation of NPIs is necessary to flatten the epidemic curve. Assuming 20% of the population have been vaccinated, the optimal period to relax NPIs would be a few days from the last peak. Regarding the prioritisation of age groups to be vaccinated, the model shows that it is better to vaccinate individuals aged 5-60 years and not just the elderly (over 60 years) and those in high-risk groups. This strategy could be more cost-effective for the government, as it would reduce the high costs associated with hospitalisation. In terms of vaccine distribution, the optimal strategy would be to allocate full dose to the elderly. If vaccine doses are limited, half dose followed by full dose would be sufficient for people under 40 years because whether they receive half or full dose, the reduction in hospitalisations would be similar and their death-to-case ratio is very low. CONCLUSIONS: This study could be presented as a decision support tool to help devise strategies to control the COVID-19 pandemic and help the Ministry of Health to better manage and allocate the available vaccine doses.

Individual based model for grouper populations.

Dusky groupers (Epinephelus marginatus) are characterized by a complex sex allocation strategies and overexploitation of bigger individuals. We developed an individual based model to investigate the long-term effects of density dependence on grouper population dynamics and to analyze the variabilities of extinction probabilities as a result of interacting mortalities at different life stages. We conduct several simulations with different forms of sex allocation functions and different combinations of mortality rates. The model was parametrized using data on dusky grouper populations from the literature. The most important insights produced by this simulation study are that density dependence of sex allocation is an evolutionarily stable strategy, increases the population biomass, mitigates the effect of the removal of large male and indicates a need for protection of females and flexible stages.