Global Dynamics of an SEIR Model with the Age of Infection and Vaccination

This paper is concerned with the stability of a SEIR (susceptible-exposed-infectious-recovered) model with the age of infection and vaccination. Firstly, we prove the positivity, boundedness, and asymptotic smoothness of the solutions. Next, the existence and local stability of disease-free and endemic steady states are shown. The basic reproduction number R0 is introduced. Furthermore, the global stability of the disease-free and endemic steady states is derived. Numerical simulations are shown to illustrate our theoretical results.

Infection Age as a Predictor of Epidemiological Metrics for Malaria

Background Accurate estimation of the burden of Plasmodium falciparum is essential for strategic planning for control and elimination. Due in part to the extreme heterogeneity in malaria exposure, immunity, other causes of disease, direct measurements of fever and disease attributable to malaria can be difficult. This can make a comparison of epidemiological metrics both within and between populations hard to interpret. An essential part of untangling this is an understanding of the complex time-course of malaria infections.Methods We reanalyzed malaria therapy infections in which individuals were intentionally infected with malaria parasites. In this analysis, we examined the age of an infection as a covariate describing aggregate patterns across all infections. We performed a series of piecewise linear and generalized linear regressions to highlight the infection age dependent patterns in both parasitemia and gametocytemia, and from parasitemia and gametocytemia to fever and transmission probabilities, respectively. Results The observed duration of untreated patent infection was 130 days. As infections progressed, the fraction of infections subpatent by microscopy increased steadily. The time-averaged malaria infections had three distinct phases in parasitemia: a growth phase for the first 6 days of patency, a rapid decline from day 6 to day 18, and a slowly declining chronic phase for the remaining duration of the infection. During the growth phase, parasite densities increased sharply to a peak. Densities sharply decline for a short period of time after the peak. During the chronic phase, infections declined steadily as infections age. Gametocytemia was strongly correlated with lagged asexual parasitemia. Fever rates and transmission efficiency were strongly correlated with parasitemia and gametocytemia. The comparison between raw data and prediction from the age of infection has good qualitative agreement across all quantities of interest for predicting averaged effects. Conclusion We established age of infection as a potentially useful covariate for malaria epidemiology. Infection age can be estimated given a history of exposure; accounting for exposure history may potentially provide a new way to estimate malaria-attributable fever rates, transmission efficiency, patent fraction, and more in immunologically naïve individuals such as children and people in low-transmission regions. Understanding how immune responses modify these statistical relationships is key for being able to apply these results more broadly.

Dynamics of a vector-borne model with direct transmission and age of infection.

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial di erential equation and obtain an explicit formula for the basic reproduction number R0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, R0 < 1. Endemic equilibrium exists and is locally asymptotically stable when R0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.

A non-standard numerical scheme for an age-of-infection epidemic model

<p style='text-indent:20px;'>We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the equation. The study of convergence properties and the analysis of the qualitative behavior of the numerical solution show that it preserves all the basic properties of the continuous model with no restrictive conditions on the step-length <inline-formula><tex-math id="M1">\begin{document}$ h $\end{document}</tex-math></inline-formula> of integration and that it recovers the continuous dynamic as <inline-formula><tex-math id="M2">\begin{document}$ h $\end{document}</tex-math></inline-formula> tends to zero.</p>

Projections and early-warning signals of a second wave of the COVID-19 epidemic in Illinois

We present two different scenarios for a second wave of the COVID-19 epidemic in Illinois and simulate them using our previously described age-of-infection model, calibrated to real-time hospital and deaths data. In the first scenario we assume that the parameters of the second wave in Illinois would be similar to those currently observed in other states such as Arizona, Florida, and Texas. We estimate doubling times of hospitalizations and test positivity in all states with relevant publicly available data and calculate the corresponding effective reproduction numbers for Illinois. These parameters are remarkably consistent in states with rapidly growing epidemics. We conjecture that the emergence of the second wave of the epidemic in these states can be attributed to superspreading events at large parties, crowded bars, and indoor dining. In our second, more optimistic scenario we assume changes in Illinois state policy would result in successful mitigation of superspreading events and thus would lower the effective reproduction number to the value observed in late June 2020. In this case our calculations show effective suppression of the second wave in Illinois. Our analysis also suggests that the logarithmic time derivatives of COVID-19 hospitalizations and case positivity can serve as a simple but strong early-warning signal of the onset of a second wave.

Differential Expression of Cytokine in Kadaknath and Commercial Chicken Against Coccidial Challenge

In the present investigation the relative expression of interleukins (IL)-1â, IL-2, IL-6, IL-17 and interferon (IFN)-Y genes were explored in response to coccidial challenge in Kadaknath (n=12), Cari-Vishal (n=12) and Cobb (n=12) broiler chicken using quantitative PCR. The intraepithelial lymphocytes cell of control, T1 and T2 on 4, 7 and 14d post infection (pi) were used as templates for expression of five inflammatory cytokines. The relative mean fold expression for ILâ1 ranged from 9.91± 0.14 (Kadaknath) to 119.01±0.29 (Cobb). The highest and lowest relative mean fold expression for IL-2 was observed to be 242.19±0.40 and 6.25±0.03 in Cobb at d4 and d14 pi, respectively. For IL-6 gene, the lowest relative mean fold expression was observed in Kadaknath (8.11±0.05) while the highest value was recorded in Cobb (99.04±0.92). The relative mean fold expression for IL-17 was 11.04±0.29 in Kadaknath and 197.40±0.37 in Cobb. For IFN-Y gene, the lowest relative mean fold expression was observed in Kadaknath (8.11±0.19), while the highest value was recorded in Cobb (84.74±0.25). In Cobb and Cari-Vishal broilers most cytokines (IL-1â, IL-6, IL-17 and IFN-Y) were observed to be transcribed to higher levels than Kadaknath chicken. It is concluded that the differential expression of cytokine genes in three genetic groups showed different degree of mucosal immune response to Eimeria infection and it depend upon the genetic background/genotype of birds, coccidial dosage and age of infection.