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Introduction To Dynamic Systems Theory Models And Applications

Africans pour dirty water around their houses which constitutes aquatic habitats (AH). These AH are sought by mosquitoes for larval development. Recent studies have shown the effectiveness of destroying AH around houses in reducing malaria incidence. An agent-based model is proposed for controlling malaria’s incidence through population sensitizing campaigns on the harmful effects of AH around houses. The environment is constituted of houses, AH, mosquitoes, humans, and hospital. Malaria’s spread dynamic is linked to the dynamics of humans and mosquitoes. The mosquito’s dynamic is represented by egg-laying and seeking blood. The human’s dynamic is animated by hitting mosquitoes. AH are destroyed each time by 10% of their starting number. The number of infected humans varied from 0-90 which led to a total of 1001 simulations. When the number of houses and AH is equal, the results are approximate as the field data. At each reduction of AH, the incidence and prevalence tend more and more towards 0. When there is no AH and infected humans, the prevalence and incidence are at 0. When there is no AH site, the disease disappears completely. Global destruction of AH in an environment and using many parameters in the same model are recommended.

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Agent-based modeling of malaria control through mosquito aquatic habitats management in a traditional sub-Sahara grouping

This article suggested and analyzed the transmission dynamics of malaria disease in a population using a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control strategies on the infected individuals in the population can be determined. The possible influence of exploring a single control, the combination of two, and the three controls on the spread of the disease was also investigated. Numerical simulation was carried out and pertinent findings are displayed graphically.

Mathematical modeling of malaria disease with control strategy

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria and investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa.

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Modeling and Stability Analysis of Within-Host IAV/SARS-CoV-2 Coinfection with Antibody Immunity

We modeled the impact of bed-net use and insecticide treated nets (ITNs), temperature, and treatment on malaria transmission dynamics using ordinary differential equations. To achieve this we formulated a simple model of mosquito biting rate that depends on temperature and usage of insecticides treated bed nets. We conducted global uncertainty and sensitivity analysis using Latin Hypercube Sampling (LHC) and Partial Rank Correlation Coefficient (PRCC) in order to find the most effective parameters that affect malaria transmission dynamics. We established the existence of the region where the model is epidemiologically feasible. We conducted the stability analysis of the disease-free equilibrium by the threshold parameter. We found the condition for the existence of the endemic equilibrium and provided necessary condition for its stability. Our results show that the peak of mosquitoes biting rate occurs at a range of temperature values not on a single value as previously reported in literature. The results also show that the combination of treatment and ITNs usage is the most effective intervention strategy towards control and eradication of malaria transmissions. Sensitivity analysis results indicate that the biting rate and the mosquitoes death rates are the most important parameters in the dynamics of malaria transmission.

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Modeling the Impact of Bed-Net Use and Treatment on Malaria Transmission Dynamics

We propose and analyze an epidemiological model to evaluate the effectiveness of bed nets as a prophylactic measure in malaria-endemic areas The main purpose in this work is the modeling of the aggressiveness of anopheles mosquitoes relative to the way humans use to protect themselves against bites of mosquitoes This model is a system of several differential equations: the number of equations depends on the particular assumptions of the model We compute the basic reproduction number, and show that if, the disease free equilibrium (DFE) is globally asymptotically stable on the non-negative orthant If, the system admits a unique endemic equilibrium (EE) that is globally and asymptotically stable Numerical simulations are presented corresponding to scenarios typical of malaria-endemic areas, based on data collected in the literature Finally, we discuss the relative effectiveness of different kinds of bed nets

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Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective

https://doi.org/10.1016/j.imu.2022.100978

HIV and COVID-19 co-infection: A mathematical model and optimal control

Dynamics of an two-group structured malaria transmission model

The COVID-19 epidemic is an unprecedented and major social and economic challenge worldwide due to the various restrictions. Inflow of infective immigrants have not been given prominence in several mathematical and epidemiological models. To investigate the impact of imported infection on the number of deaths, cumulative infected and cumulative asymptomatic, we formulate a mathematical model with infective immigrants and considering vaccination. The basic reproduction number of the special case of the model without immigration of infective people is derived. We varied two key factors that affect the transmission of COVID-19, namely the immigration and vaccination rates. In addition, we considered two different SARS-CoV-2 transmissibilities in order to account for new more contagious variants such as Omicron. Numerical simulations using initial conditions approximating the situation in the US when the vaccination program was starting show that increasing the vaccination rate significantly improves the outcomes regarding the number of deaths, cumulative infected and cumulative asymptomatic. Other factors are the natural recovery rates of infected and asymptomatic individuals, the waning rate of the vaccine and the vaccination rate. When the immigration rate is increased significantly, the number of deaths, cumulative infected and cumulative asymptomatic increase. Consequently, accounting for the level of inflow of infective immigrants may help health policy/decision-makers to formulate policies for public health prevention programs, especially with respect to the implementation of the stringent preventive lock down measure.

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Impact of Infective Immigrants on COVID-19 Dynamics

This work aims at a better understanding and the optimal control of the spread of the new severe acute respiratory corona virus 2 (SARS-CoV-2). A multi-scale model giving insights on the virus population dynamics, the transmission process and the infection mechanism is proposed first. Indeed, there are human to human virus transmission, human to environment virus transmission, environment to human virus transmission and self-infection by susceptible individuals. The global stability of the disease-free equilibrium is shown when a given threshold $$ {\mathcal {T}}_{0} $$
 is less or equal to 1 and the basic reproduction number $${\mathcal {R}}_{0} $$
 is calculated. A convergence index $$ {\mathcal {T}}_{1} $$
 is also defined in order to estimate the speed at which the disease extincts and an upper bound to the time of infectious extinction is given. The existence of the endemic equilibrium is conditional and its description is provided. Using Partial Rank Correlation Coefficient with a three levels fractional experimental design, the sensitivity of 
 $${\mathcal {R}}_{0} $$
 , $$ {\mathcal {T}}_{0} $$
 and $$ {\mathcal {T}}_{1}$$
 to control parameters is evaluated. Following this study, the most significant parameter is the probability of wearing mask followed by the probability of mobility and the disinfection rate. According to a functional cost taking into account economic impacts of SARS-CoV-2, optimal fighting strategies are determined and discussed. The study is applied to real and available data from Cameroon with a model fitting. After several simulations, social distancing and the disinfection frequency appear as the main elements of the optimal control strategy against SARS-CoV-2.

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Stéphane Yanick Tchoumi

Papers

Modeling the Dynamics of Malaria Transmission with Bed Net Protection Perspective

HIV and COVID-19 co-infection: A mathematical model and optimal control

Dynamics of an two-group structured malaria transmission model

Impact of Infective Immigrants on COVID-19 Dynamics

Estimation and optimal control of the multiscale dynamics of Covid-19: a case study from Cameroon.