Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in ...tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the
Plasmodium
malaria parasite and
Anopheles
mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature
Anopheles
habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven
Anopheles
lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large
increase
in the area at risk for malaria, but others predicting primarily a
shift
in the disease’s geographic range. More generally, both global and local environmental changes drove the initial emergence of
P. falciparum
as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the “million-murdering Death” of malaria.
•Modeling effect of temperature and rainfall on malaria transmission dynamics.•Malaria burden increases with increasing temperature and rainfall within a certain range.•Age-structure and reduced ...malaria susceptibility due to prior infection have marginal effect on malaria dynamics.
A new non-autonomous model is designed and used to assess the impact of variability in temperature and rainfall on the transmission dynamics of malaria in a population. In addition to adding age-structure in the host population and the dynamics of immature malaria mosquitoes, a notable feature of the new model is that recovered individuals do not revert to wholly-susceptible class (that is, recovered individuals enjoy reduced susceptibility to new malaria infection). In the absence of disease-induced mortality, the disease-free solution of the model is shown to be globally-asymptotically stable when the associated reproduction ratio is less than unity. The model has at least one positive periodic solution when the reproduction ratio exceeds unity (and the disease persists in the community in this case). Detailed uncertainty and sensitivity analysis, using mean monthly temperature and rainfall data from KwaZulu-Natal province of South Africa, shows that the top three parameters of the model that have the most influence on the disease transmission dynamics are the mosquito carrying capacity, transmission probability per contact for susceptible mosquitoes and human recovery rate. Numerical simulations of the model show that, for the KwaZulu-Natal province, malaria burden increases with increasing mean monthly temperature and rainfall in the ranges (17–25°C and 32–110 mm), respectively (and decreases with decreasing mean monthly temperature and rainfall values). In particular, transmission is maximized for mean monthly temperature and rainfall in the ranges 21–25°C and 95–125 mm. This occurs for a six-month period in KwaZulu-Natal (hence, this study suggests that anti-malaria control efforts should be intensified during this period). It is shown, for the fixed mean monthly temperature of KwaZulu-Natal, that malaria burden decreases whenever the amount of rainfall exceeds a certain threshold value. It is further shown (through sensitivity analysis and numerical simulations) that incorporating host age-structure and reduced susceptibility due to prior malaria infection has marginal effect on the transmission dynamics of the disease.
The novel coronavirus (COVID-19) that emerged from Wuhan city of China in late December 2019 continue to pose devastating public health and economic challenges across the world. Although the ...community-wide implementation of basic non-pharmaceutical intervention measures, such as social distancing, quarantine of suspected COVID-19 cases, isolation of confirmed cases, use of face masks in public, contact tracing and testing, have been quite effective in curtailing and mitigating the burden of the pandemic, it is universally believed that the use of a vaccine may be necessary to effectively curtail and eliminating COVID-19 in human populations. This study is based on the use of a mathematical model for assessing the impact of a hypothetical imperfect anti-COVID-19 vaccine on the control of COVID-19 in the United States. An analytical expression for the minimum percentage of unvaccinated susceptible individuals needed to be vaccinated in order to achieve vaccine-induced community herd immunity is derived. The epidemiological consequence of the herd immunity threshold is that the disease can be effectively controlled or eliminated if the minimum herd immunity threshold is achieved in the community. Simulations of the model, using baseline parameter values obtained from fitting the model with COVID-19 mortality data for the U.S., show that, for an anti-COVID-19 vaccine with an assumed protective efficacy of 80%, at least 82% of the susceptible US population need to be vaccinated to achieve the herd immunity threshold. The prospect of COVID-19 elimination in the US, using the hypothetical vaccine, is greatly enhanced if the vaccination program is combined with other interventions, such as face mask usage and/or social distancing. Such combination of strategies significantly reduces the level of the vaccine-induced herd immunity threshold needed to eliminate the pandemic in the US. For instance, the herd immunity threshold decreases to 72% if half of the US population regularly wears face masks in public (the threshold decreases to 46% if everyone wears a face mask).
The community lockdown measures implemented in the United States from late March to late May of 2020 resulted in a significant reduction in the community transmission of the COVID-19 pandemic ...throughout the country. However, a number of US states are currently experiencing an alarming post-lockdown resurgence of the pandemic, triggering fears for a devastating second pandemic wave. We designed a mathematical model for addressing the key question of whether or not the universal use of face masks can halt such resurgence (and possibly avert a second wave, without having to undergo another cycle of major community lockdown) in the states of Arizona, Florida, New York and the entire US. Model calibration, using cumulative mortality data for the four jurisdictions during their respective pre-lockdown and lockdown periods, show that pre-symptomatic and asymptomatically-infectious individuals are, by far, the main drivers of the COVID-19 pandemic in each of the jurisdictions. The implication of this result is that detecting and isolating individuals with clinical symptoms of the pandemic alone (even if all of them are found) may not be sufficient to effectively curtail the pandemic. To achieve such control, it is crucially-necessary that pre-symptomatic and asymptomatically-infectious individuals are rapidly detected and isolated (and their contacts rapidly traced and tested). Our study highlights the importance of early implementation of the community lockdown measures. In particular, a sizable reduction in the burden of the pandemic would have been recorded in each of the four jurisdictions if the community lockdown measures were implemented a week or two earlier. These reductions are significantly increased if the early implementation of the lockdown measures was complemented with a public face mask use strategy. With all related control measures maintained at their baseline levels, this study shows that the pandemic would have been almost completely suppressed from significantly taking off if the lockdown measures were implemented two weeks earlier, and if a sizable percentage of the residents of the four jurisdictions wore face masks during the respective lockdown periods. The burden of the second wave of the pandemic would have been reduced significantly if the lockdown measures were extended by two weeks. We simulated the pandemic in the four jurisdictions under three levels of lifting of community lockdown, namely mild, moderate and high. For the scenario where the control measures adopted are maintained at their baseline levels during the lockdown period, our simulations show that the states of Arizona and Florida will record devastating second waves of the pandemic by the end of 2020, while the state of New York and the entire US will record milder second waves. If the community lockdown measures were lifted at the mild lifting level (i.e., only limited community contacts and business activities are allowed, in comparison to the levels of these activities allowed during the corresponding lockdown period), only the state of Florida will experience a second wave. It is further shown that the severity of the projected second waves depend on the level of lifting of the community lockdown. For instance, the projected second wave for Arizona and Florida will be more severe than their respective first waves. It is further shown that, for high level of lifting of community lockdown measures, the increased use of face masks after the lockdown period greatly reduces the burden of the pandemic in each jurisdiction. In particular, for this high lockdown lifting scenario, none of the four jurisdictions will experience a second wave if half of their residents wear face masks consistently after their respective lockdown period. A diagnostic testing strategy that increases the maximum detection rate of asymptomatic infected individuals (followed by contact tracing and self-isolation of the detected cases) greatly reduces the burden of the pandemic in all four jurisdictions, particularly if also combined with a universal face mask use strategy. Finally, it is shown that the universal use of face masks in public, with at least moderate level of compliance, could halt the post-lockdown resurgence of COVID-19, in addition to averting the potential for (and severity of) a second wave of the pandemic in each of the four jurisdictions.
A mathematical model is designed and used to study the transmission dynamics and control of COVID-19 in Nigeria. The model, which was rigorously analysed and parametrized using COVID-19 data ...published by the Nigeria Centre for Disease Control (NCDC), was used to assess the community-wide impact of various control and mitigation strategies in some jurisdictions within Nigeria (notably the states of Kano and Lagos, and the Federal Capital Territory, Abuja). Numerical simulations of the model showed that COVID-19 can be effectively controlled in Nigeria using moderate levels of social-distancing strategy in the jurisdictions and in the entire nation. Although the use of face masks in public can significantly reduce COVID-19 in Nigeria, its use, as a sole intervention strategy, may fail to lead to a substantial reduction in disease burden. Such substantial reduction is feasible in the jurisdictions (and the entire Nigerian nation) if the public face mask use strategy is complemented with a social-distancing strategy. The community lockdown measures implemented in Nigeria on March 30, 2020 need to be maintained for at least three to four months to lead to the effective containment of COVID-19 outbreaks in the country. Relaxing, or fully lifting, the lockdown measures sooner, in an effort to re-open the economy or the country, may trigger a deadly second wave of the pandemic.
The novel coronavirus (COVID-19) pandemic that emerged from Wuhan city in December 2019 overwhelmed health systems and paralyzed economies around the world. It became the most important public health ...challenge facing mankind since the 1918 Spanish flu pandemic. Various theoretical and empirical approaches have been designed and used to gain insight into the transmission dynamics and control of the pandemic. This study presents a primer for formulating, analysing and simulating mathematical models for understanding the dynamics of COVID-19. Specifically, we introduce simple compartmental, Kermack-McKendrick-type epidemic models with homogeneously- and heterogeneously-mixed populations, an endemic model for assessing the potential population-level impact of a hypothetical COVID-19 vaccine. We illustrate how some basic non-pharmaceutical interventions against COVID-19 can be incorporated into the epidemic model. A brief overview of other kinds of models that have been used to study the dynamics of COVID-19, such as agent-based, network and statistical models, is also presented. Possible extensions of the basic model, as well as open challenges associated with the formulation and theoretical analysis of models for COVID-19 dynamics, are suggested.
The great successes recorded in the fight against malaria over the last two decades, resulting from the wide scale implementation of insecticide-based interventions in malaria-endemic areas, has ...prompted a renewed global effort to eradicate malaria. The widespread emergence of insecticide resistance in the population of adult female malaria mosquitoes is considered to pose a potential challenge to such effort. In this study, we address one of the key questions in malaria ecology, namely whether or not insecticide resistance increase malaria transmission. We developed a genetics-epidemiology modeling framework that incorporates a detailed genotype structure of the gene that confers insecticide resistance in mosquitoes, malaria epidemiology in mosquitoes and humans (stratified based on whether or not they are protected by Long-lasting insecticide-treated nets (LLINs) indoors), genotype-specific mosquito repellance property of LLINs and mosquito biting behavior (indoor and outdoor bites). Conditions for the existence and local asymptotic stability of the various disease-free equilibria (by genotype) of the resulting genetic-epidemiology model are derived. This study identifies four parameters of the model that play a crucial role on quantifying the impact of insecticide resistance on malaria transmission, namely the parameters related to the level of the dominance of the resistant allele in heterozygous mosquitoes, the coverage of long-lasting insecticidal nets in the community, the probability of endophilic mosquitoes to successfully take a bloodmeal indoors and the proportion of new adult mosquitoes that are endophilic. We showed that, depending on the values of these four identified parameters, insecticide resistance can increase, decrease, or have no effect on malaria transmission. Our simulations show that malaria eradication can indeed be achieved using the currently-available chemical insecticides, even in the wake of the prevailing widespread insecticide resistance in malaria-endemic areas, if the insecticide-based interventions implemented can result in the attainment of the optimal values of the four identified parameters in malaria-endemic areas.
A new stage-structured model for the population dynamics of the mosquito (a major vector for numerous vector-borne diseases), which takes the form of a deterministic system of non-autonomous ...nonlinear differential equations, is designed and used to study the effect of variability in temperature and rainfall on mosquito abundance in a community. Two functional forms of eggs oviposition rate, namely the Verhulst-Pearl logistic and Maynard-Smith-Slatkin functions, are used. Rigorous analysis of the autonomous version of the model shows that, for any of the oviposition functions considered, the trivial equilibrium of the model is locally- and globally-asymptotically stable if a certain vectorial threshold quantity is less than unity. Conditions for the existence and global asymptotic stability of the non-trivial equilibrium solutions of the model are also derived. The model is shown to undergo a Hopf bifurcation under certain conditions (and that increased density-dependent competition in larval mortality reduces the likelihood of such bifurcation). The analyses reveal that the Maynard-Smith-Slatkin oviposition function sustains more oscillations than the Verhulst-Pearl logistic function (hence, it is more suited, from ecological viewpoint, for modeling the egg oviposition process). The non-autonomous model is shown to have a globally-asymptotically stable trivial periodic solution, for each of the oviposition functions, when the associated reproduction threshold is less than unity. Furthermore, this model, in the absence of density-dependent mortality rate for larvae, has a unique and globally-asymptotically stable periodic solution under certain conditions. Numerical simulations of the non-autonomous model, using mosquito surveillance and weather data from the Peel region of Ontario, Canada, show a peak mosquito abundance for temperature and rainfall values in the range
20
-
25
∘
C and 15–35 mm, respectively. These ranges are recorded in the Peel region between July and August (hence, this study suggests that anti-mosquito control effects should be intensified during this period).
•A new epidemiology-genetics model for assessing the role of insecticides resistance (due to widespread use of insecticides treated bednets (ITNs) and indoors residual spraying (IRS)) on malaria is ...presented.•Model incorporates several fitness costs of insecticide resistance.•Effective size of ITNs and IRS coverage required for effective disease control and management of resstance depenends on level of resistance allele dominance and several fitness costs of resistance.
Although the widespread use of indoors residual spraying (IRS) and insecticides treated bednets (ITNs; later replaced by long-lasting insecticidal nets (LLINs)) has led to a dramatic reduction of malaria burden in endemic areas, such usage has also resulted in the major challenge of the evolution of insecticide resistance in the mosquito population in those areas. Thus, efforts to combat malaria also include the urgent problem of effectively managing insecticide resistance. This study is based on the design and analysis of a new mathematical model for assessing the impact of insecticides resistance in the mosquito population (due to widespread use of IRS and ITNs) on the transmission dynamics and control of malaria in a community. The model, which couples disease epidemiology with vector population genetics, incorporates several fitness costs associated with insecticide resistance. Detailed rigorous analysis of the model is presented. Using data and parameter values relevant to malaria dynamics in moderate and high malaria transmission settings in some parts of Ethiopia, simulations of the model show that, while the ITNs-IRS strategy can lead to the effective control of the disease in both the moderate and high malaria transmission setting if the ITNs coverage level in the community is high enough (regardless of the level of IRS coverage), it fails to manage insecticide resistance (as measured in terms of the frequency of resistant allele at equilibrium in the community). It is further shown that the effective size of the coverage level of the ITNs and IRS required to effectively control the disease, while effectively managing insecticide resistance in the mosquito population, depends on the magnitude of the level of resistant allele dominance (in mosquitoes with heterozygous genotype) and several fitness costs associated with the insecticide resistance in the vector population. For instance, in a moderate transmission setting, malaria burden can be reduced to low levels of endemicity (even with low coverage of ITNs and IRS), and insecticide resistance effectively managed, if the fitness costs of resistance are at their assumed baseline values. Such reduction is not achievable if the fitness costs of resistance are lower than the baseline values.
•Vaccine-derived herd immunity against COVID-19 can be achieved if at least 60% of the population is fully-vaccinated.•COVID-19 elimination is feasible by June 2022 if the current baseline full ...vaccination coverage is increased by about 20%.•Elimination prospects are improved significantly if vaccination is combined with the use of moderate to high-quality masks.•Having more people wear surgical masks is more beneficial than having fewer people wear the highly-effective N95 masks.•Treatment of symptomatic individuals has a significant impact on reducing daily hospitalizations.
The effectiveness of control interventions against COVID-19 is threatened by the emergence of SARS-CoV-2 variants of concern. We present a mathematical model for studying the transmission dynamics of two of these variants (Delta and Omicron) in the United States, in the presence of vaccination, treatment of individuals with clinical symptoms of the disease and the use of face masks. The model is parameterized and cross-validated using observed daily case data for COVID-19 in the United States for the period from November 2021 (when Omicron first emerged) to March 2022. Rigorous qualitative analysis of the model shows that the disease-free equilibrium of the model is locally-asymptotically stable when the control reproduction number of the model (denoted by Rc) is less than one. This equilibrium is shown to be globally-asymptotically stable for a special case of the model, where disease-induced mortality is negligible and both vaccine-derived immunity in fully-vaccinated individuals and natural immunity do not wane, when the associated reproduction number is less than one. The epidemiological implication of the latter result is that the combined vaccination-boosting strategy can lead to the elimination of the pandemic if its implementation can bring (and maintain) the associated reproduction number to a value less than one. An analytical expression for the vaccine-derived herd immunity threshold is derived. Using this expression, together with the baseline values of the parameters of the parameterized model, we showed that the vaccine-derived herd immunity can be achieved in the United States (so that the pandemic will be eliminated) if at least 68% of the population is fully-vaccinated with two of the three vaccines approved for use in the United States (Pfizer or Moderna vaccine). Furthermore, this study showed (as of the time of writing in March 2022) that the control reproduction number of the Omicron variant was approximately 3.5 times that of the Delta variant (the reproduction of the latter is computed to be ≈0.2782), indicating that Delta had practically died out and that Omicron has competitively-excluded Delta (to become the predominant variant in the United States). Based on our analysis and parameterization at the time of writing of this paper (March 2022), our study suggests that SARS-CoV-2 elimination is feasible by June 2022 if the current baseline level of the coverage of fully-vaccinated individuals is increased by about 20%. The prospect of pandemic elimination is significantly improved if vaccination is combined with a face mask strategy that prioritizes moderately effective and high-quality masks. Having a high percentage of the populace wearing the moderately-effective surgical mask is more beneficial to the community than having low percentage of the populace wearing the highly-effective N95 masks. We showed that waning natural and vaccine-derived immunity (if considered individually) offer marginal impact on disease burden, except for the case when they wane at a much faster rate (e.g., within three months), in comparison to the baseline (estimated to be within 9 months to a year). Treatment of symptomatic individuals has marginal effect in reducing daily cases of SARS-CoV-2, in comparison to the baseline, but it has significant impact in reducing daily hospitalizations. Furthermore, while treatment significantly reduces daily hospitalizations (and, consequently, deaths), the prospects of COVID-19 elimination in the United States are significantly enhanced if investments in control resources are focused on mask usage and vaccination rather than on treatment.
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