A Mathematical Modeling Study: Assessing Impact of Mismatch Between Influenza Vaccine Strains and Circulating Strains in Hajj

How heterogeneity in density dependence affects disease spread: when lifestyle matters

People's lifestyles play a major role in disease risk. Some employment sectors and transport modes involve fixed exposures regardless of community size, while in other settings exposure tracks with population density. MERS-CoV, a coronavirus discovered in Saudi Arabia in 2012 closely related to those causing SARS and COVID-19, appears to need extended contact time for transmission, making some segments of a community at greater risk than others. We model mathematically how heterogeneity in contact rate structure impacts disease spread, using as a case study a MERS outbreak in two Saudi Arabian communities. We divide the at-risk population into segments with exposure rates either independent of population density or density-dependent. Analysis shows disease spread is minimized for intermediate size populations with a limited proportion of individuals in the density-independent group. In the case study, the high proportion of density-independent exposure may explain the historical outbreak's extinction in the larger city.

Impact of vaccine measures on the transmission dynamics of COVID-19

In many nations, efforts to prevent and control COVID-19 have been significantly impeded by the SARS-CoV-2 virus ongoing mutation. The Omicron strain, a more recent and prevalent strain, has had more significant detrimental effects in countries worldwide. To investigate the impact of the Omicron BA.2 strain on vaccine efficacy, we proposed a model with vaccination and immunological decline in this research. Then, we fitted our model based on the number of daily new instances reported by the government in Jilin and Shanghai, China. We estimated the effective reproduction number Re = 4.71 for the Jilin and Re = 3.32 for Shanghai. Additionally, we do sensitivity analysis to identify the critical factors affecting the effective reproduction number Re. It was found that vaccination rate, effectiveness rate, and declining rate had a significant effect on Re. Further, we investigate the relevant parameter thresholds that make Re lower than unity. Finally, rich numerical experiments were then carried out. We observed that even when vaccine efficiency was not high, increasing vaccination rates had a significant effect on early disease transmission, that limiting social distance was the most economical and rational measure to control the spread of disease, and that for a short period, reducing immune decline was not significant in curbing disease transmission.

Global investigation for an "SIS" model for COVID-19 epidemic with asymptomatic infection

In this paper, we analyse a dynamical system taking into account the asymptomatic infection and we consider optimal control strategies based on a regular network. We obtain basic mathematical results for the model without control. We compute the basic reproduction number (R) by using the method of the next generation matrix then we analyse the local stability and global stability of the equilibria (disease-free equilibrium (DFE) and endemic equilibrium (EE)). We prove that DFE is LAS (locally asymptotically stable) when R<1 and it is unstable when R>1. Further, the existence, the uniqueness and the stability of EE is carried out. We deduce that when R>1, EE exists and is unique and it is LAS. By using generalized Bendixson-Dulac theorem, we prove that DFE is GAS (globally asymptotically stable) if R<1 and that the unique endemic equilibrium is globally asymptotically stable when R>1. Later, by using Pontryagin's maximum principle, we propose several reasonable optimal control strategies to the control and the prevention of the disease. We mathematically formulate these strategies. The unique optimal solution was expressed using adjoint variables. A particular numerical scheme was applied to solve the control problem. Finally, several numerical simulations that validate the obtained results were presented.

How influenza vaccination and virus interference may impact combined influenza-coronavirus disease burden

Demand for influenza vaccine rose as countries prepared for the second COVID-19 wave over the winter months of 2020-2021. High coverage of the influenza vaccine can significantly reduce morbidity and mortality of the burden of influenza. Natural influenza infection creates short-term non-specific immunity against respiratory viruses (virus interference). We model two viral diseases, both of the SEIR type, to investigate whether the influenza vaccine increases the combined disease burden of influenza and COVID-19 in a dual outbreak. We show that the combined disease burden’s behavior depends on virus interference factors and the proportion of the population vaccinated against influenza. Our results indicate that influenza vaccination only lowers the overall disease burden when net virus interference is relatively low.