Dynamic analysis of a malaria reaction-diffusion model with periodic delays and vector bias

<abstract><p>One of the most important vector-borne disease in humans is malaria, caused by <italic>Plasmodium</italic> parasite. Seasonal temperature elements have a major effect on the life development of mosquitoes and the development of parasites. In this paper, we establish and analyze a reaction-diffusion model, which includes seasonality, vector-bias, temperature-dependent extrinsic incubation period (EIP) and maturation delay in mosquitoes. In order to get the model threshold dynamics, a threshold parameter, the basic reproduction number $ R_{0} $ is introduced, which is the spectral radius of the next generation operator. Quantitative analysis indicates that when $ R_{0} &lt; 1 $, there is a globally attractive disease-free $ \omega $-periodic solution; disease is uniformly persistent in humans and mosquitoes if $ R_{0} &gt; 1 $. Numerical simulations verify the results of the theoretical analysis and discuss the effects of diffusion and seasonality. We study the relationship between the parameters in the model and $ R_{0} $. More importantly, how to allocate medical resources to reduce the spread of disease is explored through numerical simulations. Last but not least, we discover that when studying malaria transmission, ignoring vector-bias or assuming that the maturity period is not affected by temperature, the risk of disease transmission will be underestimate.</p></abstract>

Threshold Dynamics of a Diffusive Herpes Model Incorporating Fixed Relapse Period in a Spatial Heterogeneous Environment

In this paper, we aim to establish the threshold-type dynamics of a diffusive herpes model that assumes a fixed relapse period and nonlinear recovery rate. It turns out that when considering diseases with a fixed relapse period, the diffusion of recovered individuals will lead to nonlocal recovery term. We characterize the basic reproduction number, ℜ 0 , for the model through the next generation operator approach. Moreover, in a homogeneous case, we calculate the ℜ 0 explicitly. By utilizing the principal eigenvalue of the associated eigenvalue problem or equivalently by ℜ 0 , we establish the threshold-type dynamics of the model in the sense that the herpes is either extinct or close to the epidemic value. Numerical simulations are performed to verify the theoretical results and the effects of the spatial heterogeneity on disease transmission.

Transmission dynamics and optimal control of H7N9 in China

H7N9 avian influenza is a highly pathogenic zoonotic disease. In order to control the disease, many strategies have been adopted in China such as poultry culling, the closure of live poultry markets (LPMs), the vaccination of poultry, and the treatment for humans. Due to the limited resource, it is of paramount significance to achieve the optimal control. In this paper, an epidemic model incorporating the selective culling rate is formulated to investigate the transmission mechanism of H7N9. The threshold dynamics and bifurcation analyses of the model are well investigated. Furthermore, the problem of optimal control is explored in line with Pontryagin’s Maximum Principle, with consideration given to the comprehensive measures. The numerical simulations suggest that the vaccination of poultry and the closure of LPMs are the two most economical and effective measures.

On the Dynamics of a Fractional-Order Ebola Epidemic Model with Nonlinear Incidence Rates

We propose a new fractional-order model to investigate the transmission and spread of Ebola virus disease. The proposed model incorporates relevant biological factors that characterize Ebola transmission during an outbreak. In particular, we have assumed that susceptible individuals are capable of contracting the infection from a deceased Ebola patient due to traditional beliefs and customs practiced in many African countries where frequent outbreaks of the disease are recorded. We conducted both epidemic and endemic analysis, with a focus on the threshold dynamics characterized by the basic reproduction number. Model parameters were estimated based on the 2014-2015 Ebola outbreak in Sierra Leone. In addition, numerical simulation results are presented to demonstrate the analytical findings.

Data-driven multi-scale mathematical modeling of SARS-CoV-2 infection reveals heterogeneity among COVID-19 patients

Patients with coronavirus disease 2019 (COVID-19) often exhibit diverse disease progressions associated with various infectious ability, symptoms, and clinical treatments. To systematically and thoroughly understand the heterogeneous progression of COVID-19, we developed a multi-scale computational model to quantitatively understand the heterogeneous progression of COVID-19 patients infected with severe acute respiratory syndrome (SARS)-like coronavirus (SARS-CoV-2). The model consists of intracellular viral dynamics, multicellular infection process, and immune responses, and was formulated using a combination of differential equations and stochastic modeling. By integrating multi-source clinical data with model analysis, we quantified individual heterogeneity using two indexes, i.e., the ratio of infected cells and incubation period. Specifically, our simulations revealed that increasing the host antiviral state or virus induced type I interferon (IFN) production rate can prolong the incubation period and postpone the transition from asymptomatic to symptomatic outcomes. We further identified the threshold dynamics of T cell exhaustion in the transition between mild-moderate and severe symptoms, and that patients with severe symptoms exhibited a lack of naïve T cells at a late stage. In addition, we quantified the efficacy of treating COVID-19 patients and investigated the effects of various therapeutic strategies. Simulations results suggested that single antiviral therapy is sufficient for moderate patients, while combination therapies and prevention of T cell exhaustion are needed for severe patients. These results highlight the critical roles of IFN and T cell responses in regulating the stage transition during COVID-19 progression. Our study reveals a quantitative relationship underpinning the heterogeneity of transition stage during COVID-19 progression and can provide a potential guidance for personalized therapy in COVID-19 patients.

Identification of Complement-Related Missense Variants in Pediatric Patients with Acute and Post COVID-19 Syndromes

Background: Complement dysregulation has been documented in the molecular pathophysiology of COVID-19 and recently implicated in the relevant pediatric patient inflammatory responses. Aims: Based on our previous data in adults, we hypothesized that signatures of complement genetic variants would also be detectable in pediatric patients exhibiting COVID-19 signs and symptoms. Methods: We prospectively studied consecutive pediatric patients from our COVID-19 Units (November 2020-March 2021). COVID-19 was confirmed by reverse-transcriptase polymerase chain reaction (RT-PCR). Patient data were recorded by treating physicians that followed patients up to discharge. DNA was obtained from peripheral blood samples. Probes were designed using the Design studio (Illumina). Amplicons cover exons of complement-associated genes (C3, C5, CFB, CFD, CFH, CFHR1, CFI, CD46, CD55, MBL2, MASP1, MASP2, COLEC11, FCN1, FCN3 as well as ADAMTS13 and ΤHBD) spanning 15 bases into introns. We used 10ng of initial DNA material. Libraries were quantified using Qubit and sequenced on a MiniSeq System in a 2x150 bp run. Analysis was performed using the TruSeq Amplicon application (BaseSpace). Alignment was based on the banded Smith-Waterman algorithm in the targeted regions (specified in a manifest file). We performed variant calling with the Illumina-developed Somatic Variant Caller in germline mode and variant allele frequency higher than 20%. Both Ensembl and Refseq were used for annotation of the output files. A preliminary analysis (A) for the identification of variants of clinical significance was based on annotated ClinVar data, while a further and more selective analysis (B) was performed to identify missense complement coding variants that may biochemically contribute to the deregulation of innate responses during infection. This analysis was mainly based on the dbSNP and UniProt databases and available literature. Results: We studied 80 children and adolescents, 8 of whom developed inflammatory syndromes (MIS-C group). Among them, 41 were hospitalized and eventually all survived. In our preliminary analysis, patients exhibited heterogeneous variant profiles including pathogenic, benign, likely benign, and variants of unknown significance (median number of variants: 97, range: 61-103). We found a variant of ADAMTS13 (rs2301612, missense) in 39 patients. We also detected two missense risk factor variants, previously detected in complement-related diseases: rs2230199 in C3 (33 patients); and rs800292 in CFH (36 patients). Among them, 40 patients had a combination of these characterized variants. This combination was significantly associated with the presence of dyspnea (p=0.031) and cough (p=0.042). Furthermore, 27 patients had a pathogenic variant in MBL2 (rs1800450), and 7 a pathogenic deletion in FCN3 that have been previously associated with inflammatory syndromes.The results of our further analysis are summarized in Figure. We identified common variants, some well represented by relatively high frequencies (&gt;70%) (rs11098044 in CFI, rs1061170 in CFH and rs12711521 in MASP2) and others less abundant, but varying considerably between the hospitalized group, the non-admitted group and the MIS-C individuals (rs2230199 in C3, rs1065489 in CFH, rs12614 and rs641153 in CFB, rs1800450 in MBL2, rs2273346 and rs72550870 in MASP2, rs72549154 in MASP3 and rs7567833 in COLEC11, all highlighted in Figure in red).). Structurally, the majority of these common variants of interest encode charge reversal mutations. These may influence protein-protein interactions in complex formations that are important for complement activation and/or regulation. Conclusion: In pediatric COVID-19 we have detected a novel set of complement missense coding variants some of which have been implicated earlier in inflammatory syndromes and endothelial stress responses. Certain combinations of mutations of alternative and/or lectin pathway components may increase the threshold dynamics of complement consumption and therefore alter COVID-19 phenotypes. Figure 1 Figure 1. Disclosures Gavriilaki: Alexion, Omeros, Sanofi Corporation: Consultancy; Gilead Corporation: Honoraria; Pfizer Corporation: Research Funding. Anagnostopoulos: Abbvie: Other: clinical trials; Sanofi: Other: clinical trials ; Ocopeptides: Other: clinical trials ; GSK: Other: clinical trials; Incyte: Other: clinical trials ; Takeda: Other: clinical trials ; Amgen: Other: clinical trials ; Janssen: Other: clinical trials; novartis: Other: clinical trials; Celgene: Other: clinical trials; Roche: Other: clinical trials; Astellas: Other: clinical trials .

Wave propagation in a diffusive SEIR epidemic model with nonlocal transmission and a general nonlinear incidence rate

We introduce a diffusive SEIR model with nonlocal delayed transmission between the infected subpopulation and the susceptible subpopulation with a general nonlinear incidence. We show that our results on existence and nonexistence of traveling wave solutions are determined by the basic reproduction number $R_{0}=\partial _{I}F(S_{0},0)/\gamma $ R 0 = ∂ I F ( S 0 , 0 ) / γ of the corresponding ordinary differential equations and the minimal wave speed $c^{*}$ c ∗ . The main difficulties lie in the fact that the semiflow generated here does not admit the order-preserving property. In the present paper, we overcome these difficulties to obtain the threshold dynamics. In view of the numerical simulations, we also obtain that the minimal wave speed is explicitly determined by the time delay and nonlocality in disease transmission and by the spatial movement pattern of the exposed and infected individuals.