A MATHEMATICAL ANALYSIS OF ZIKA VIRUS EPIDEMIC IN RIO DE JANEIRO AS A VECTOR-BORNE AND SEXUALLY TRANSMITTED DISEASE

2019 ◽  
Vol 27 (01) ◽  
pp. 83-105 ◽  
Author(s):  
GUSTAVO CRUZ-PACHECO ◽  
LOURDES ESTEVA ◽  
CLAUDIA PIO FERREIRA
Keyword(s):  
Basic Reproduction Number ◽  
Zika Virus ◽  
Disease Transmission ◽  
Rio De Janeiro ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sexual Transmission ◽  
Transmitted Disease ◽  
Infectious Period ◽  
Sexually Transmitted

In this work we formulate a mathematical model to assess the importance of sexual transmission during the Zika virus outbreak that occurred in Rio de Janeiro, Brazil, in 2015. To this end, we deduce from the model an analytical expression of the basic reproduction number of Zika, [Formula: see text], in terms of the vectorial and sexual transmissions, and we use the estimations given in Ref. 1 [Villela DAM, Bastos LS, de Carvalho LM, Cruz OG, Gomes MFC, Durovni B, Lemos MC, Saraceni V, Coelho FC, Codeço CT, Zika in Rio de Janeiro: Assessment of basic reproduction number and comparison with dengue outbreaks, Epidemiol Infect 145(8):1649–1657, 2017] for the [Formula: see text] values of Zika virus and dengue virus epidemics in Rio de Janeiro to evaluate the contribution of sexual transmission of Zika virus. According to the obtained results, sexual transmission (pure plus mediated by vector transmission) contributes from 23% to 46% for the [Formula: see text] increment. Also, an asymmetric sexual transmission between men and women can explain the fact that the incidence of Zika virus in women was 60% higher than in man during the 2015 epidemics. We also carry out a sensitivity analysis using [Formula: see text] as the output parameter. The results of this analysis have shown that the transmission rate between human and mosquito populations, the mosquito mortality rate, and the human infectious period are the parameters that contribute more to the [Formula: see text] variation, highlighting the importance of vector control to halt disease transmission.

scholarly journals The Effect of Seasonal Weather Variation on the Dynamics of the Plague Disease

2017 ◽  
Vol 2017 ◽  
pp. 1-25 ◽  
Author(s):  
Rigobert C. Ngeleja ◽  
Livingstone S. Luboobi ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Weather Conditions ◽  
Effective Control ◽  
Human Beings ◽  
Weather Variation ◽  
The Basic Reproduction Number ◽  
Seasonal Weather

Plague is a historic disease which is also known to be the most devastating disease that ever occurred in human history, caused by gram-negative bacteria known as Yersinia pestis. The disease is mostly affected by variations of weather conditions as it disturbs the normal behavior of main plague disease transmission agents, namely, human beings, rodents, fleas, and pathogens, in the environment. This in turn changes the way they interact with each other and ultimately leads to a periodic transmission of plague disease. In this paper, we formulate a periodic epidemic model system by incorporating seasonal transmission rate in order to study the effect of seasonal weather variation on the dynamics of plague disease. We compute the basic reproduction number of a proposed model. We then use numerical simulation to illustrate the effect of different weather dependent parameters on the basic reproduction number. We are able to deduce that infection rate, progression rates from primary forms of plague disease to more severe forms of plague disease, and the infectious flea abundance affect, to a large extent, the number of bubonic, septicemic, and pneumonic plague infective agents. We recommend that it is more reasonable to consider these factors that have been shown to have a significant effect on RT for effective control strategies.

scholarly journals Tracing DAY-ZERO and Forecasting the Fade out of the COVID-19 Outbreak in Lombardy, Italy: A Compartmental Modelling and Numerical Optimization Approach

2020 ◽  
Author(s):  
Lucia Russo ◽  
Cleo Anastassopoulou ◽  
Athanasios Tsakris ◽  
Gennaro Nicola Bifulco ◽  
Emilio Fortunato Campana ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Total Population ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Cumulative Number ◽  
Community Mobility ◽  
The Basic Reproduction Number

AbstractItaly currently constitutes the epicenter of the novel coronavirus disease (COVID-19) pandemic, having surpassed China’s death toll. The disease is sweeping through Lombardy, which remains in lockdown since the 8th of March. As of the same day, the isolation measures taken in Lombardy have been extended to the entire country. Here, we provide estimates for: (a) the DAY-ZERO of the outbreak in Lombardy, Italy; (b) the actual number of exposed/infected cases in the total population; (c) the basic reproduction number (R0); (d) the “effective” per-day disease transmission; and, importantly, (e) a forecast for the fade out of the outbreak, on the basis of the COVID-19 Community Mobility Reports released by Google on March 29.MethodsTo deal with the uncertainty in the number of actual exposed/ infected cases in the total population, we address a compartmental Susceptible/ Exposed/ Infectious/ Recovered/ Dead (SEIRD) model with two compartments of infectious persons: one modelling the total cases in the population and another modelling the confirmed cases. The parameters of the model corresponding to the recovery period, the time from the onset of symptoms to death, the case fatality ratio, and the time from exposure to the time that an individual starts to be infectious, have been set as reported from clinical studies on COVID-For the estimation of the DAY-ZERO of the outbreak in Lombardy, as well as of the “effective” per-day transmission rate for which no clinical data are available, we have used the SEIRD simulator to fit the numbers of new daily cases from February 21 to the 8th of March, the lockdown day of Lombardy and of all Italy. This was accomplished by solving a mixed-integer optimization problem with the aid of genetic algorithms. Based on the computed values, we also provide an estimation of the basic reproduction number R0. Furthermore, based on an estimation for the reduction in the “effective” transmission rate of the disease as of March 8 that reflects the suspension of almost all activities in Italy, we ran the simulator to forecast the fade out of the epidemic. For this purpose, we considered the reduction in mobility in Lombardy as released on March 29 by Google COVID-19 Community Mobility Reports, the effect of social distancing, and the draconian measures taken by the government on March 20 and March 21, 2020.ResultsBased on the proposed methodological procedure, we estimated that the DAY-ZERO was most likely between January 5 and January 23 with the most probable date the 15th of January 2020. The actual cumulative number of exposed cases in the total population in Lombardy on March 8 was of the order of 15 times the confirmed cumulative number of infected cases. The “effective” per-day disease transmission rate for the period until March 8 was found to be 0.686 (95% CI:0.660, 0.713), while the basic reproduction number R0 was found to be 4.51 (95% CI: 4.14, 4.90).Importantly, simulations show that the COVID-19 pandemic in Lombardy is expected to fade out by the end of May -early June, 2020, if the draconian, as of March 20 and March 21, measures are maintained.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals From Mosquito Bites to Sexual Transmission: Evaluating Mouse Models of Zika Virus Infection

Viruses ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2244
Author(s):  
Elizabeth Balint ◽  
Amelia Montemarano ◽  
Emily Feng ◽  
Ali A. Ashkar
Keyword(s):  
Mouse Models ◽  
Zika Virus ◽  
Reproductive Tract ◽  
Sexual Transmission ◽  
Zikv Infection ◽  
Sexually Transmitted ◽  
Advantages And Disadvantages ◽  
Effective Use ◽  
The Impact ◽  
Male To Female

Following the recent outbreak of Zika virus (ZIKV) infections in Latin America, ZIKV has emerged as a global health threat due to its ability to induce neurological disease in both adults and the developing fetus. ZIKV is largely mosquito-borne and is now endemic in many parts of Africa, Asia, and South America. However, several reports have demonstrated persistent ZIKV infection of the male reproductive tract and evidence of male-to-female sexual transmission of ZIKV. Sexual transmission may broaden the reach of ZIKV infections beyond its current geographical limits, presenting a significant threat worldwide. Several mouse models of ZIKV infection have been developed to investigate ZIKV pathogenesis and develop effective vaccines and therapeutics. However, the majority of these models focus on mosquito-borne infection, while few have considered the impact of sexual transmission on immunity and pathogenesis. This review will examine the advantages and disadvantages of current models of mosquito-borne and sexually transmitted ZIKV and provide recommendations for the effective use of ZIKV mouse models.

scholarly journals Optimal Control of a Dengue-Dengvaxia Model: Comparison Between Vaccination and Vector Control

2021 ◽  
Vol 9 (1) ◽  
pp. 198-212
Author(s):  
Cheryl Q. Mentuda
Keyword(s):  
Optimal Control ◽  
Vector Control ◽  
Basic Reproduction Number ◽  
Human Population ◽  
Model Comparison ◽  
Reproduction Number ◽  
Control Strategies ◽  
Minimum Principle ◽  
Transmitted Disease ◽  
The Basic Reproduction Number

Abstract Dengue is the most common mosquito-borne viral infection transmitted disease. It is due to the four types of viruses (DENV-1, DENV-2, DENV-3, DENV-4), which transmit through the bite of infected Aedes aegypti and Aedes albopictus female mosquitoes during the daytime. The first globally commercialized vaccine is Dengvaxia, also known as the CYD-TDV vaccine, manufactured by Sanofi Pasteur. This paper presents a Ross-type epidemic model to describe the vaccine interaction between humans and mosquitoes using an entomological mosquito growth population and constant human population. After establishing the basic reproduction number ℛ0, we present three control strategies: vaccination, vector control, and the combination of vaccination and vector control. We use Pontryagin’s minimum principle to characterize optimal control and apply numerical simulations to determine which strategies best suit each compartment. Results show that vector control requires shorter time applications in minimizing mosquito populations. Whereas vaccinating the primary susceptible human population requires a shorter time compared to the secondary susceptible human.

scholarly journals On an SEIR Epidemic Model with Vaccination of Newborns and Periodic Impulsive Vaccination with Eventual On-Line Adapted Vaccination Strategies to the Varying Levels of the Susceptible Subpopulation

2020 ◽  
Vol 10 (22) ◽  
pp. 8296 ◽  
Author(s):  
Malen Etxeberria-Etxaniz ◽  
Santiago Alonso-Quesada ◽  
Manuel De la Sen
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Impulsive Vaccination ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper investigates a susceptible-exposed-infectious-recovered (SEIR) epidemic model with demography under two vaccination effort strategies. Firstly, the model is investigated under vaccination of newborns, which is fact in a direct action on the recruitment level of the model. Secondly, it is investigated under a periodic impulsive vaccination on the susceptible in the sense that the vaccination impulses are concentrated in practice in very short time intervals around a set of impulsive time instants subject to constant inter-vaccination periods. Both strategies can be adapted, if desired, to the time-varying levels of susceptible in the sense that the control efforts be increased as those susceptible levels increase. The model is discussed in terms of suitable properties like the positivity of the solutions, the existence and allocation of equilibrium points, and stability concerns related to the values of the basic reproduction number. It is proven that the basic reproduction number lies below unity, so that the disease-free equilibrium point is asymptotically stable for larger values of the disease transmission rates under vaccination controls compared to the case of absence of vaccination. It is also proven that the endemic equilibrium point is not reachable if the disease-free one is stable and that the disease-free equilibrium point is unstable if the reproduction number exceeds unity while the endemic equilibrium point is stable. Several numerical results are investigated for both vaccination rules with the option of adapting through ime the corresponding efforts to the levels of susceptibility. Such simulation examples are performed under parameterizations related to the current SARS-COVID 19 pandemic.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

2015 ◽  
Vol 23 (03) ◽  
pp. 423-455
Author(s):  
P. MOUOFO TCHINDA ◽  
JEAN JULES TEWA ◽  
BOULECHARD MEWOLI ◽  
SAMUEL BOWONG
Keyword(s):  
Drug Therapy ◽  
Hepatitis B ◽  
Basic Reproduction Number ◽  
Disease Transmission ◽  
Time Delays ◽  
Reproduction Number ◽  
Distributed Delay ◽  
Global Dynamics ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

scholarly journals The effect of heterogeneous infectious period and contagiousness on the dynamics ofSalmonellatransmission in dairy cattle

2008 ◽  
Vol 136 (11) ◽  
pp. 1496-1510 ◽  
Author(s):  
C. LANZAS ◽  
S. BRIEN ◽  
R. IVANEK ◽  
Y. LO ◽  
P. P. CHAPAGAIN ◽  
...  
Keyword(s):  
Dairy Cattle ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Dynamics ◽  
Infectious Period ◽  
Specific Group ◽  
Infection Transmission ◽  
Force Of Infection ◽  
The Impact

SUMMARYThe objective of this study was to address the impact of heterogeneity of infectious period and contagiousness onSalmonellatransmission dynamics in dairy cattle populations. We developed three deterministic SIR-type models with two basic infected stages (clinically and subclinically infected). In addition, model 2 included long-term shedders, which were defined as individuals with low contagiousness but long infectious period, and model 3 included super-shedders (individuals with high contagiousness and long infectious period). The simulated dynamics, basic reproduction number (R0) and critical vaccination threshold were studied. Clinically infected individuals were the main force of infection transmission for models 1 and 2. Long-term shedders had a small impact on the transmission of the infection and on the estimated vaccination thresholds. The presence of super-shedders increasesR0and decreases the effectiveness of population-wise strategies to reduce infection, making necessary the application of strategies that target this specific group.

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